#include <math.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include "ran_tg.h"

double ran_tg_zig4000(gsl_rng *r,double a)
{
// Simulate x~N(0,1), subject to x>a, using generator r
// Zig's method

    /* Insert here */
    //****************************
#define N 4001 //total number of vertical boxes
#define I0 3271
#define INVH 1631.73284006
#define AMIN -2.00443204036
#define AMAX 2.60545795099

static const double x[4002]={
-2.00443204036, -1.99990455547, -1.99541747213, -1.99096998962, 
-1.98656133124, -1.98219074335, -1.97785749442, -1.97356087419, 
-1.96930019287, -1.96507478031, -1.96088398528, -1.95672717477, 
-1.95260373328, -1.9485130622, -1.94445457918, -1.94042771755, 
-1.93643192574, -1.93246666677, -1.92853141772, -1.92462566922, 
-1.92074892503, -1.91690070156, -1.91308052741, -1.90928794302, 
-1.90552250025, -1.90178376197, -1.89807130174, -1.89438470345, 
-1.89072356098, -1.88708747787, -1.88347606705, -1.8798889505, 
-1.87632575899, -1.87278613181, -1.86926971649, -1.86577616858, 
-1.86230515137, -1.85885633567, -1.8554293996, -1.85202402837, 
-1.84863991405, -1.84527675539, -1.84193425762, -1.83861213227, 
-1.83531009698, -1.83202787533, -1.82876519668, -1.825521796, 
-1.82229741372, -1.81909179558, -1.81590469249, -1.81273586036, 
-1.80958506, -1.80645205698, -1.8033366215, -1.80023852827, 
-1.79715755637, -1.79409348917, -1.79104611422, -1.78801522309, 
-1.78500061134, -1.78200207837, -1.77901942732, -1.77605246501, 
-1.77310100183, -1.77016485166, -1.76724383175, -1.7643377627, 
-1.7614464683, -1.75856977555, -1.75570751448, -1.75285951816, 
-1.75002562257, -1.74720566658, -1.74439949184, -1.74160694276, 
-1.73882786639, -1.7360621124, -1.73330953303, -1.73056998298, 
-1.72784331941, -1.72512940185, -1.72242809217, -1.71973925449, 
-1.71706275519, -1.7143984628, -1.71174624799, -1.70910598353, 
-1.70647754419, -1.70386080677, -1.70125565, -1.69866195455, 
-1.69607960292, -1.69350847947, -1.69094847035, -1.68839946345, 
-1.6858613484, -1.68333401649, -1.68081736069, -1.67831127556, 
-1.67581565725, -1.67333040348, -1.67085541345, -1.6683905879, 
-1.665935829, -1.66349104035, -1.66105612696, -1.65863099522, 
-1.65621555288, -1.65380970898, -1.65141337389, -1.64902645924, 
-1.64664887792, -1.64428054402, -1.64192137286, -1.63957128092, 
-1.63723018585, -1.63489800643, -1.63257466256, -1.63026007522, 
-1.62795416649, -1.62565685948, -1.62336807836, -1.62108774828, 
-1.61881579544, -1.61655214696, -1.61429673098, -1.61204947656, 
-1.60981031368, -1.60757917325, -1.60535598708, -1.60314068784, 
-1.60093320909, -1.59873348523, -1.59654145149, -1.59435704393, 
-1.59218019943, -1.59001085565, -1.58784895103, -1.58569442477, 
-1.58354721686, -1.581407268, -1.57927451964, -1.57714891392, 
-1.57503039371, -1.57291890258, -1.57081438477, -1.56871678519, 
-1.56662604942, -1.56454212368, -1.56246495486, -1.56039449044, 
-1.55833067854, -1.55627346789, -1.55422280782, -1.55217864825, 
-1.55014093969, -1.5481096332, -1.54608468043, -1.54406603357, 
-1.54205364536, -1.54004746908, -1.53804745854, -1.53605356807, 
-1.53406575252, -1.53208396723, -1.53010816806, -1.52813831134, 
-1.52617435391, -1.52421625305, -1.52226396655, -1.52031745264, 
-1.51837667, -1.51644157777, -1.51451213554, -1.51258830332, 
-1.51067004156, -1.50875731112, -1.5068500733, -1.50494828979, 
-1.50305192269, -1.50116093452, -1.49927528818, -1.49739494693, 
-1.49551987447, -1.49365003484, -1.49178539245, -1.48992591209, 
-1.48807155892, -1.48622229844, -1.48437809651, -1.48253891934, 
-1.48070473348, -1.47887550581, -1.47705120356, -1.47523179427, 
-1.47341724582, -1.47160752641, -1.46980260454, -1.46800244903, 
-1.46620702902, -1.46441631394, -1.46263027351, -1.46084887778, 
-1.45907209704, -1.45729990192, -1.4555322633, -1.45376915236, 
-1.45201054053, -1.45025639954, -1.44850670139, -1.44676141832, 
-1.44502052286, -1.44328398779, -1.44155178613, -1.43982389118, 
-1.43810027647, -1.43638091579, -1.43466578316, -1.43295485285, 
-1.43124809936, -1.42954549744, -1.42784702206, -1.4261526484, 
-1.42446235191, -1.42277610822, -1.42109389321, -1.41941568296, 
-1.41774145377, -1.41607118216, -1.41440484485, -1.41274241877, 
-1.41108388106, -1.40942920906, -1.40777838029, -1.40613137251, 
-1.40448816364, -1.40284873181, -1.40121305532, -1.39958111269, 
-1.3979528826, -1.39632834393, -1.39470747574, -1.39309025725, 
-1.39147666789, -1.38986668723, -1.38826029505, -1.38665747129, 
-1.38505819603, -1.38346244956, -1.38187021232, -1.3802814649, 
-1.37869618807, -1.37711436276, -1.37553597004, -1.37396099116, 
-1.37238940752, -1.37082120066, -1.36925635228, -1.36769484423, 
-1.36613665852, -1.36458177727, -1.3630301828, -1.36148185752, 
-1.35993678401, -1.35839494499, -1.35685632332, -1.35532090198, 
-1.3537886641, -1.35225959295, -1.35073367192, -1.34921088453, 
-1.34769121444, -1.34617464545, -1.34466116145, -1.34315074649, 
-1.34164338473, -1.34013906045, -1.33863775808, -1.33713946213, 
-1.33564415726, -1.33415182822, -1.33266245992, -1.33117603734, 
-1.3296925456, -1.32821196994, -1.32673429568, -1.32525950829, 
-1.32378759331, -1.32231853644, -1.32085232344, -1.31938894019, 
-1.3179283727, -1.31647060705, -1.31501562944, -1.31356342618, 
-1.31211398366, -1.31066728839, -1.30922332698, -1.30778208612, 
-1.30634355261, -1.30490771336, -1.30347455533, -1.30204406564, 
-1.30061623144, -1.29919104001, -1.29776847873, -1.29634853503, 
-1.29493119647, -1.29351645068, -1.29210428538, -1.29069468838, 
-1.28928764758, -1.28788315096, -1.28648118658, -1.2850817426, 
-1.28368480725, -1.28229036885, -1.2808984158, -1.27950893658, 
-1.27812191975, -1.27673735394, -1.27535522788, -1.27397553036, 
-1.27259825027, -1.27122337654, -1.2698508982, -1.26848080436, 
-1.26711308419, -1.26574772695, -1.26438472195, -1.26302405859, 
-1.26166572634, -1.26030971474, -1.25895601339, -1.25760461198, 
-1.25625550025, -1.25490866802, -1.25356410517, -1.25222180165, 
-1.25088174749, -1.24954393277, -1.24820834764, -1.24687498231, 
-1.24554382707, -1.24421487225, -1.24288810826, -1.24156352558, 
-1.24024111474, -1.23892086632, -1.23760277098, -1.23628681945, 
-1.23497300248, -1.23366131092, -1.23235173565, -1.23104426764, 
-1.22973889789, -1.22843561746, -1.22713441748, -1.22583528914, 
-1.22453822366, -1.22324321234, -1.22195024653, -1.22065931762, 
-1.21937041707, -1.2180835364, -1.21679866716, -1.21551580096, 
-1.21423492948, -1.21295604444, -1.21167913759, -1.21040420078, 
-1.20913122586, -1.20786020475, -1.20659112944, -1.20532399194, 
-1.20405878432, -1.2027954987, -1.20153412724, -1.20027466216, 
-1.19901709572, -1.19776142023, -1.19650762804, -1.19525571156, 
-1.19400566322, -1.19275747553, -1.19151114101, -1.19026665225, 
-1.18902400188, -1.18778318256, -1.18654418701, -1.18530700798, 
-1.18407163828, -1.18283807074, -1.18160629825, -1.18037631374, 
-1.17914811017, -1.17792168055, -1.17669701793, -1.1754741154, 
-1.17425296609, -1.17303356317, -1.17181589985, -1.17059996938, 
-1.16938576505, -1.16817328018, -1.16696250814, -1.16575344233, 
-1.1645460762, -1.16334040321, -1.16213641689, -1.16093411079, 
-1.1597334785, -1.15853451364, -1.15733720988, -1.1561415609, 
-1.15494756045, -1.1537552023, -1.15256448023, -1.1513753881, 
-1.15018791978, -1.14900206916, -1.1478178302, -1.14663519686, 
-1.14545416315, -1.14427472312, -1.14309687083, -1.14192060039, 
-1.14074590595, -1.13957278166, -1.13840122174, -1.13723122041, 
-1.13606277195, -1.13489587064, -1.13373051083, -1.13256668686, 
-1.13140439313, -1.13024362405, -1.12908437408, -1.12792663769, 
-1.1267704094, -1.12561568374, -1.12446245528, -1.12331071862, 
-1.12216046839, -1.12101169923, -1.11986440583, -1.1187185829, 
-1.11757422519, -1.11643132745, -1.11528988448, -1.11414989111, 
-1.11301134218, -1.11187423257, -1.11073855719, -1.10960431095, 
-1.10847148882, -1.10734008578, -1.10621009684, -1.10508151703, 
-1.10395434141, -1.10282856507, -1.10170418311, -1.10058119068, 
-1.09945958293, -1.09833935506, -1.09722050226, -1.09610301977, 
-1.09498690286, -1.09387214681, -1.09275874692, -1.09164669853, 
-1.09053599698, -1.08942663766, -1.08831861598, -1.08721192734, 
-1.08610656721, -1.08500253104, -1.08389981434, -1.08279841262, 
-1.08169832142, -1.0805995363, -1.07950205283, -1.07840586663, 
-1.07731097332, -1.07621736855, -1.07512504799, -1.07403400732, 
-1.07294424226, -1.07185574854, -1.07076852192, -1.06968255816, 
-1.06859785307, -1.06751440246, -1.06643220217, -1.06535124805, 
-1.06427153597, -1.06319306184, -1.06211582157, -1.06103981109, 
-1.05996502636, -1.05889146336, -1.05781911808, -1.05674798653, 
-1.05567806475, -1.05460934878, -1.0535418347, -1.0524755186, 
-1.05141039657, -1.05034646476, -1.04928371929, -1.04822215635, 
-1.04716177209, -1.04610256273, -1.04504452448, -1.04398765357, 
-1.04293194626, -1.04187739881, -1.04082400752, -1.03977176868, 
-1.03872067861, -1.03767073366, -1.03662193018, -1.03557426455, 
-1.03452773314, -1.03348233237, -1.03243805866, -1.03139490845, 
-1.03035287819, -1.02931196435, -1.02827216342, -1.02723347191, 
-1.02619588633, -1.02515940322, -1.02412401912, -1.02308973062, 
-1.02205653428, -1.02102442671, -1.01999340452, -1.01896346433, 
-1.01793460279, -1.01690681657, -1.01588010232, -1.01485445675, 
-1.01382987655, -1.01280635844, -1.01178389916, -1.01076249545, 
-1.00974214407, -1.0087228418, -1.00770458543, -1.00668737176, 
-1.00567119762, -1.00465605983, -1.00364195524, -1.00262888071, 
-1.00161683312, -1.00060580935, -0.999595806306, -0.9985868209, 
-0.997578850062, -0.996571890733, -0.995565939868, -0.994560994436, 
-0.993557051418, -0.992554107808, -0.991552160613, -0.990551206854, 
-0.989551243564, -0.988552267788, -0.987554276585, -0.986557267027, 
-0.985561236196, -0.984566181188, -0.983572099113, -0.982578987091, 
-0.981586842254, -0.980595661749, -0.979605442731, -0.978616182371, 
-0.977627877849, -0.976640526359, -0.975654125105, -0.974668671305, 
-0.973684162186, -0.972700594988, -0.971717966963, -0.970736275374, 
-0.969755517495, -0.968775690612, -0.967796792022, -0.966818819033, 
-0.965841768964, -0.964865639146, -0.963890426921, -0.962916129641, 
-0.961942744669, -0.960970269379, -0.959998701157, -0.959028037398, 
-0.958058275508, -0.957089412906, -0.956121447017, -0.955154375281, 
-0.954188195145, -0.953222904069, -0.952258499521, -0.951294978982, 
-0.95033233994, -0.949370579895, -0.948409696358, -0.947449686847, 
-0.946490548893, -0.945532280036, -0.944574877824, -0.943618339818, 
-0.942662663587, -0.941707846709, -0.940753886774, -0.939800781378, 
-0.93884852813, -0.937897124647, -0.936946568555, -0.935996857491, 
-0.9350479891, -0.934099961035, -0.933152770962, -0.932206416553, 
-0.931260895491, -0.930316205466, -0.929372344179, -0.928429309338, 
-0.927487098664, -0.926545709881, -0.925605140727, -0.924665388946, 
-0.923726452292, -0.922788328527, -0.921851015421, -0.920914510754, 
-0.919978812315, -0.919043917899, -0.918109825313, -0.917176532369, 
-0.916244036888, -0.915312336703, -0.91438142965, -0.913451313577, 
-0.912521986339, -0.911593445799, -0.910665689828, -0.909738716305, 
-0.908812523118, -0.907887108163, -0.906962469342, -0.906038604567, 
-0.905115511758, -0.90419318884, -0.90327163375, -0.902350844428, 
-0.901430818827, -0.900511554903, -0.899593050622, -0.898675303958, 
-0.897758312891, -0.896842075409, -0.895926589508, -0.895011853191, 
-0.894097864469, -0.893184621359, -0.892272121887, -0.891360364086, 
-0.890449345995, -0.889539065661, -0.888629521138, -0.887720710488, 
-0.886812631779, -0.885905283087, -0.884998662493, -0.884092768089, 
-0.883187597969, -0.882283150238, -0.881379423006, -0.88047641439, 
-0.879574122514, -0.878672545509, -0.877771681512, -0.876871528668, 
-0.875972085128, -0.875073349049, -0.874175318595, -0.873277991937, 
-0.872381367254, -0.871485442727, -0.870590216549, -0.869695686916, 
-0.868801852031, -0.867908710104, -0.86701625935, -0.866124497993, 
-0.865233424261, -0.864343036389, -0.863453332618, -0.862564311196, 
-0.861675970376, -0.860788308418, -0.859901323588, -0.859015014157, 
-0.858129378404, -0.857244414613, -0.856360121074, -0.855476496083, 
-0.854593537942, -0.853711244958, -0.852829615446, -0.851948647726, 
-0.851068340122, -0.850188690965, -0.849309698594, -0.84843136135, 
-0.847553677583, -0.846676645646, -0.845800263899, -0.844924530708, 
-0.844049444444, -0.843175003483, -0.842301206208, -0.841428051007, 
-0.840555536273, -0.839683660404, -0.838812421805, -0.837941818885, 
-0.83707185006, -0.83620251375, -0.83533380838, -0.834465732382, 
-0.833598284192, -0.832731462252, -0.831865265009, -0.830999690914, 
-0.830134738426, -0.829270406006, -0.828406692123, -0.827543595248, 
-0.826681113861, -0.825819246443, -0.824957991484, -0.824097347476, 
-0.823237312917, -0.82237788631, -0.821519066163, -0.82066085099, 
-0.819803239307, -0.818946229639, -0.818089820512, -0.817234010459, 
-0.816378798017, -0.815524181729, -0.814670160142, -0.813816731806, 
-0.812963895279, -0.812111649122, -0.8112599919, -0.810408922185, 
-0.80955843855, -0.808708539576, -0.807859223848, -0.807010489955, 
-0.806162336489, -0.805314762049, -0.804467765238, -0.803621344663, 
-0.802775498936, -0.801930226672, -0.801085526493, -0.800241397023, 
-0.799397836891, -0.798554844732, -0.797712419183, -0.796870558888, 
-0.796029262492, -0.795188528648, -0.79434835601, -0.793508743238, 
-0.792669688996, -0.791831191953, -0.790993250781, -0.790155864155, 
-0.789319030758, -0.788482749274, -0.787647018393, -0.786811836806, 
-0.785977203212, -0.785143116312, -0.784309574812, -0.783476577421, 
-0.782644122852, -0.781812209823, -0.780980837056, -0.780150003277, 
-0.779319707213, -0.7784899476, -0.777660723175, -0.776832032678, 
-0.776003874855, -0.775176248455, -0.774349152231, -0.773522584939, 
-0.772696545341, -0.7718710322, -0.771046044284, -0.770221580367, 
-0.769397639223, -0.768574219631, -0.767751320376, -0.766928940243, 
-0.766107078024, -0.765285732513, -0.764464902507, -0.763644586809, 
-0.762824784223, -0.762005493558, -0.761186713627, -0.760368443246, 
-0.759550681234, -0.758733426414, -0.757916677614, -0.757100433662, 
-0.756284693394, -0.755469455646, -0.754654719259, -0.753840483077, 
-0.753026745948, -0.752213506722, -0.751400764255, -0.750588517404, 
-0.74977676503, -0.748965505998, -0.748154739176, -0.747344463435, 
-0.746534677651, -0.7457253807, -0.744916571465, -0.74410824883, 
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1.20913122586, 1.21040420078, 1.21167913759, 1.21295604444, 
1.21423492948, 1.21551580096, 1.21679866716, 1.2180835364, 
1.21937041707, 1.22065931762, 1.22195024653, 1.22324321234, 
1.22453822366, 1.22583528914, 1.22713441748, 1.22843561746, 
1.22973889789, 1.23104426764, 1.23235173565, 1.23366131092, 
1.23497300248, 1.23628681945, 1.23760277098, 1.23892086632, 
1.24024111474, 1.24156352558, 1.24288810826, 1.24421487225, 
1.24554382707, 1.24687498231, 1.24820834764, 1.24954393277, 
1.25088174749, 1.25222180165, 1.25356410517, 1.25490866802, 
1.25625550025, 1.25760461198, 1.25895601339, 1.26030971474, 
1.26166572634, 1.26302405859, 1.26438472195, 1.26574772695, 
1.26711308419, 1.26848080436, 1.2698508982, 1.27122337654, 
1.27259825027, 1.27397553036, 1.27535522788, 1.27673735394, 
1.27812191975, 1.27950893658, 1.2808984158, 1.28229036885, 
1.28368480725, 1.2850817426, 1.28648118658, 1.28788315096, 
1.28928764758, 1.29069468838, 1.29210428538, 1.29351645068, 
1.29493119647, 1.29634853503, 1.29776847873, 1.29919104001, 
1.30061623144, 1.30204406564, 1.30347455533, 1.30490771336, 
1.30634355261, 1.30778208612, 1.30922332698, 1.31066728839, 
1.31211398366, 1.31356342618, 1.31501562944, 1.31647060705, 
1.3179283727, 1.31938894019, 1.32085232344, 1.32231853644, 
1.32378759331, 1.32525950829, 1.32673429568, 1.32821196994, 
1.3296925456, 1.33117603734, 1.33266245992, 1.33415182822, 
1.33564415726, 1.33713946213, 1.33863775808, 1.34013906045, 
1.34164338473, 1.34315074649, 1.34466116145, 1.34617464545, 
1.34769121444, 1.34921088453, 1.35073367192, 1.35225959295, 
1.3537886641, 1.35532090198, 1.35685632332, 1.35839494499, 
1.35993678401, 1.36148185752, 1.3630301828, 1.36458177727, 
1.36613665852, 1.36769484423, 1.36925635228, 1.37082120066, 
1.37238940752, 1.37396099116, 1.37553597004, 1.37711436276, 
1.37869618807, 1.3802814649, 1.38187021232, 1.38346244956, 
1.38505819603, 1.38665747129, 1.38826029505, 1.38986668723, 
1.39147666789, 1.39309025725, 1.39470747574, 1.39632834393, 
1.3979528826, 1.39958111269, 1.40121305532, 1.40284873181, 
1.40448816364, 1.40613137251, 1.40777838029, 1.40942920906, 
1.41108388106, 1.41274241877, 1.41440484485, 1.41607118216, 
1.41774145377, 1.41941568296, 1.42109389321, 1.42277610822, 
1.42446235191, 1.4261526484, 1.42784702206, 1.42954549744, 
1.43124809936, 1.43295485285, 1.43466578316, 1.43638091579, 
1.43810027647, 1.43982389118, 1.44155178613, 1.44328398779, 
1.44502052286, 1.44676141832, 1.44850670139, 1.45025639954, 
1.45201054053, 1.45376915236, 1.4555322633, 1.45729990192, 
1.45907209704, 1.46084887778, 1.46263027351, 1.46441631394, 
1.46620702902, 1.46800244903, 1.46980260454, 1.47160752641, 
1.47341724582, 1.47523179427, 1.47705120356, 1.47887550581, 
1.48070473348, 1.48253891934, 1.48437809651, 1.48622229844, 
1.48807155892, 1.48992591209, 1.49178539245, 1.49365003484, 
1.49551987447, 1.49739494693, 1.49927528818, 1.50116093452, 
1.50305192269, 1.50494828979, 1.5068500733, 1.50875731112, 
1.51067004156, 1.51258830332, 1.51451213554, 1.51644157777, 
1.51837667, 1.52031745264, 1.52226396655, 1.52421625305, 
1.52617435391, 1.52813831134, 1.53010816806, 1.53208396723, 
1.53406575252, 1.53605356807, 1.53804745854, 1.54004746908, 
1.54205364536, 1.54406603357, 1.54608468043, 1.5481096332, 
1.55014093969, 1.55217864825, 1.55422280782, 1.55627346789, 
1.55833067854, 1.56039449044, 1.56246495486, 1.56454212368, 
1.56662604942, 1.56871678519, 1.57081438477, 1.57291890258, 
1.57503039371, 1.57714891392, 1.57927451964, 1.581407268, 
1.58354721686, 1.58569442477, 1.58784895103, 1.59001085565, 
1.59218019943, 1.59435704393, 1.59654145149, 1.59873348523, 
1.60093320909, 1.60314068784, 1.60535598708, 1.60757917325, 
1.60981031368, 1.61204947656, 1.61429673098, 1.61655214696, 
1.61881579544, 1.62108774828, 1.62336807836, 1.62565685948, 
1.62795416649, 1.63026007522, 1.63257466256, 1.63489800643, 
1.63723018585, 1.63957128092, 1.64192137286, 1.64428054402, 
1.64664887792, 1.64902645924, 1.65141337389, 1.65380970898, 
1.65621555288, 1.65863099522, 1.66105612696, 1.66349104035, 
1.665935829, 1.6683905879, 1.67085541345, 1.67333040348, 
1.67581565725, 1.67831127556, 1.68081736069, 1.68333401649, 
1.6858613484, 1.68839946345, 1.69094847035, 1.69350847947, 
1.69607960292, 1.69866195455, 1.70125565, 1.70386080677, 
1.70647754419, 1.70910598353, 1.71174624799, 1.7143984628, 
1.71706275519, 1.71973925449, 1.72242809217, 1.72512940185, 
1.72784331941, 1.73056998298, 1.73330953303, 1.7360621124, 
1.73882786639, 1.74160694276, 1.74439949184, 1.74720566658, 
1.75002562257, 1.75285951816, 1.75570751448, 1.75856977555, 
1.7614464683, 1.7643377627, 1.76724383175, 1.77016485166, 
1.77310100183, 1.77605246501, 1.77901942732, 1.78200207837, 
1.78500061134, 1.78801522309, 1.79104611422, 1.79409348917, 
1.79715755637, 1.80023852827, 1.8033366215, 1.80645205698, 
1.80958506, 1.81273586036, 1.81590469249, 1.81909179558, 
1.82229741372, 1.825521796, 1.82876519668, 1.83202787533, 
1.83531009698, 1.83861213227, 1.84193425762, 1.84527675539, 
1.84863991405, 1.85202402837, 1.8554293996, 1.85885633567, 
1.86230515137, 1.86577616858, 1.86926971649, 1.87278613181, 
1.87632575899, 1.8798889505, 1.88347606705, 1.88708747787, 
1.89072356098, 1.89438470345, 1.89807130174, 1.90178376197, 
1.90552250025, 1.90928794302, 1.91308052741, 1.91690070156, 
1.92074892503, 1.92462566922, 1.92853141772, 1.93246666677, 
1.93643192574, 1.94042771755, 1.94445457918, 1.9485130622, 
1.95260373328, 1.95672717477, 1.96088398528, 1.96507478031, 
1.96930019287, 1.97356087419, 1.97785749442, 1.98219074335, 
1.98656133124, 1.99096998962, 1.99541747213, 1.99990455547, 
2.00443204036, 2.00900075251, 2.01361154371, 2.01826529295, 
2.02296290758, 2.02770532458, 2.03249351185, 2.03732846962, 
2.04221123192, 2.0471428681, 2.05212448451, 2.05715722623, 
2.06224227888, 2.06738087065, 2.07257427429, 2.07782380938, 
2.08313084465, 2.08849680045, 2.09392315145, 2.09941142942, 
2.10496322628, 2.11058019727, 2.11626406445, 2.12201662031, 
2.12783973172, 2.13373534416, 2.13970548619, 2.14575227431, 
2.15187791816, 2.1580847261, 2.16437511125, 2.17075159793, 
2.17721682871, 2.18377357191, 2.19042472984, 2.1971733476, 
2.20402262267, 2.21097591537, 2.21803676019, 2.22520887808, 
2.23249618993, 2.23990283128, 2.24743316835, 2.25509181569, 
2.26288365549, 2.27081385882, 2.27888790909, 2.28711162784, 
2.29549120334, 2.30403322228, 2.31274470495, 2.32163314439, 
2.33070655011, 2.33997349698, 2.34944318006, 2.35912547628, 
2.36903101398, 2.37917125159, 2.3895585669, 2.40020635872, 
2.411129163, 2.422342786, 2.43386445755, 2.44571300825, 
2.45790907518, 2.47047534177, 2.48343681896, 2.49682117646, 
2.51065913523, 2.52498493519, 2.53983689632, 2.55525809634, 
2.57129719532, 2.58800944712, 2.60545795099, 2.62371521493, 
2.64286512889, 2.66300548366, 2.68425122698, 2.7067387311, 
2.73063147325, 2.75612772826, 2.78347119119, 2.81296597401, 
2.84499832124, 2.8800689917, 2.91884323355, 2.9622311235, 
3.0115232357, 3.06863405379, 3.13657337257, 3.22045475765, 
3.32996541598, 3.48672170399};

static const double yl[4001]={
0.053513975472, 0.0540012735356, 0.0544874991381, 0.054972661389, 
0.0554567692269, 0.0559398314244, 0.0564218565922, 0.0569028531841, 
0.0573828295011, 0.0578617936955, 0.0583397537752, 0.058816717607, 
0.059292692921, 0.0597676873138, 0.060241708252, 0.0607147630756, 
0.0611868590013, 0.0616580031256, 0.0621282024276, 0.0625974637723, 
0.0630657939132, 0.0635331994951, 0.0639996870564, 0.0644652630325, 
0.0649299337573, 0.0653937054663, 0.0658565842984, 0.0663185762986, 
0.0667796874201, 0.0672399235259, 0.0676992903918, 0.0681577937072, 
0.0686154390782, 0.0690722320286, 0.0695281780022, 0.0699832823643, 
0.0704375504035, 0.0708909873334, 0.0713435982942, 0.0717953883543, 
0.0722463625114, 0.0726965256949, 0.0731458827663, 0.0735944385211, 
0.0740421976905, 0.074489164942, 0.0749353448811, 0.0753807420524, 
0.0758253609412, 0.076269205974, 0.0767122815202, 0.0771545918932, 
0.077596141351, 0.0780369340979, 0.0784769742851, 0.078916266012, 
0.0793548133268, 0.0797926202279, 0.0802296906646, 0.080666028538, 
0.081101637702, 0.081536521964, 0.0819706850859, 0.082404130785, 
0.0828368627345, 0.0832688845646, 0.0837001998631, 0.0841308121761, 
0.084560725009, 0.0849899418268, 0.0854184660553, 0.0858463010813, 
0.0862734502535, 0.0866999168832, 0.0871257042449, 0.0875508155769, 
0.0879752540816, 0.0883990229268, 0.0888221252457, 0.0892445641375, 
0.0896663426683, 0.0900874638713, 0.0905079307475, 0.0909277462662, 
0.0913469133655, 0.0917654349529, 0.0921833139053, 0.0926005530704, 
0.0930171552661, 0.0934331232819, 0.0938484598786, 0.0942631677893, 
0.0946772497194, 0.0950907083474, 0.095503546325, 0.0959157662776, 
0.0963273708049, 0.0967383624809, 0.0971487438546, 0.0975585174503, 
0.0979676857678, 0.098376251283, 0.098784216448, 0.0991915836918, 
0.0995983554201, 0.100004534016, 0.100410121841, 0.100815121233, 
0.10121953451, 0.101623363968, 0.102026611881, 0.102429280502, 
0.102831372066, 0.103232888785, 0.103633832853, 0.104034206444, 
0.10443401171, 0.104833250787, 0.105231925791, 0.10563003882, 
0.106027591953, 0.106424587249, 0.106821026753, 0.10721691249, 
0.107612246467, 0.108007030675, 0.108401267088, 0.108794957663, 
0.10918810434, 0.109580709043, 0.109972773679, 0.110364300142, 
0.110755290307, 0.111145746034, 0.111535669171, 0.111925061545, 
0.112313924974, 0.112702261257, 0.113090072181, 0.113477359516, 
0.113864125022, 0.11425037044, 0.1146360975, 0.115021307918, 
0.115406003396, 0.115790185624, 0.116173856276, 0.116557017014, 
0.11693966949, 0.117321815339, 0.117703456185, 0.118084593641, 
0.118465229306, 0.118845364768, 0.1192250016, 0.119604141367, 
0.119982785621, 0.120360935901, 0.120738593735, 0.121115760642, 
0.121492438126, 0.121868627682, 0.122244330795, 0.122619548937, 
0.12299428357, 0.123368536146, 0.123742308106, 0.124115600881, 
0.12448841589, 0.124860754545, 0.125232618245, 0.12560400838, 
0.125974926331, 0.126345373469, 0.126715351154, 0.127084860738, 
0.127453903564, 0.127822480963, 0.128190594259, 0.128558244767, 
0.128925433793, 0.129292162631, 0.129658432571, 0.130024244891, 
0.13038960086, 0.130754501741, 0.131118948787, 0.131482943242, 
0.131846486342, 0.132209579317, 0.132572223385, 0.132934419758, 
0.133296169642, 0.13365747423, 0.134018334713, 0.13437875227, 
0.134738728074, 0.13509826329, 0.135457359075, 0.135816016581, 
0.13617423695, 0.136532021316, 0.13688937081, 0.137246286551, 
0.137602769653, 0.137958821225, 0.138314442365, 0.138669634167, 
0.139024397717, 0.139378734095, 0.139732644373, 0.140086129618, 
0.14043919089, 0.140791829241, 0.141144045718, 0.141495841361, 
0.141847217205, 0.142198174276, 0.142548713597, 0.142898836183, 
0.143248543043, 0.143597835179, 0.14394671359, 0.144295179266, 
0.144643233193, 0.144990876349, 0.14533810971, 0.145684934242, 
0.146031350908, 0.146377360665, 0.146722964463, 0.147068163249, 
0.147412957962, 0.147757349537, 0.148101338903, 0.148444926984, 
0.148788114699, 0.149130902961, 0.149473292678, 0.149815284753, 
0.150156880085, 0.150498079565, 0.150838884082, 0.151179294519, 
0.151519311753, 0.151858936658, 0.152198170101, 0.152537012946, 
0.152875466051, 0.153213530271, 0.153551206454, 0.153888495445, 
0.154225398084, 0.154561915205, 0.15489804764, 0.155233796214, 
0.155569161751, 0.155904145066, 0.156238746972, 0.156572968279, 
0.156906809791, 0.157240272307, 0.157573356623, 0.15790606353, 
0.158238393817, 0.158570348265, 0.158901927654, 0.159233132759, 
0.159563964351, 0.159894423197, 0.160224510058, 0.160554225695, 
0.160883570863, 0.161212546311, 0.161541152788, 0.161869391036, 
0.162197261796, 0.162524765803, 0.162851903789, 0.163178676483, 
0.163505084608, 0.163831128886, 0.164156810034, 0.164482128766, 
0.164807085792, 0.165131681818, 0.165455917548, 0.165779793681, 
0.166103310913, 0.166426469936, 0.16674927144, 0.167071716111, 
0.167393804631, 0.167715537679, 0.16803691593, 0.168357940058, 
0.168678610731, 0.168998928615, 0.169318894373, 0.169638508664, 
0.169957772145, 0.170276685469, 0.170595249286, 0.170913464242, 
0.171231330982, 0.171548850146, 0.171866022373, 0.172182848295, 
0.172499328546, 0.172815463755, 0.173131254545, 0.173446701542, 
0.173761805364, 0.174076566628, 0.174390985949, 0.174705063937, 
0.175018801202, 0.175332198348, 0.175645255979, 0.175957974695, 
0.176270355092, 0.176582397766, 0.176894103309, 0.177205472308, 
0.177516505351, 0.177827203022, 0.178137565902, 0.178447594568, 
0.178757289598, 0.179066651564, 0.179375681037, 0.179684378585, 
0.179992744774, 0.180300780166, 0.180608485323, 0.180915860803, 
0.18122290716, 0.181529624949, 0.18183601472, 0.182142077022, 
0.182447812399, 0.182753221396, 0.183058304554, 0.183363062412, 
0.183667495505, 0.183971604368, 0.184275389534, 0.18457885153, 
0.184881990885, 0.185184808123, 0.185487303768, 0.185789478338, 
0.186091332353, 0.186392866329, 0.186694080779, 0.186994976215, 
0.187295553146, 0.18759581208, 0.187895753521, 0.188195377973, 
0.188494685937, 0.188793677911, 0.189092354391, 0.189390715873, 
0.18968876285, 0.189986495811, 0.190283915244, 0.190581021638, 
0.190877815475, 0.191174297238, 0.191470467408, 0.191766326463, 
0.192061874879, 0.192357113132, 0.192652041693, 0.192946661033, 
0.193240971621, 0.193534973925, 0.193828668408, 0.194122055533, 
0.194415135763, 0.194707909556, 0.19500037737, 0.195292539661, 
0.195584396882, 0.195875949485, 0.196167197921, 0.196458142637, 
0.196748784081, 0.197039122697, 0.197329158929, 0.197618893218, 
0.197908326003, 0.198197457722, 0.198486288812, 0.198774819706, 
0.199063050838, 0.199350982639, 0.199638615537, 0.199925949961, 
0.200212986337, 0.200499725089, 0.20078616664, 0.20107231141, 
0.20135815982, 0.201643712287, 0.201928969228, 0.202213931056, 
0.202498598186, 0.202782971029, 0.203067049994, 0.20335083549, 
0.203634327924, 0.203917527701, 0.204200435225, 0.204483050898, 
0.204765375121, 0.205047408293, 0.205329150811, 0.205610603072, 
0.205891765471, 0.2061726384, 0.206453222252, 0.206733517417, 
0.207013524284, 0.207293243239, 0.20757267467, 0.207851818961, 
0.208130676495, 0.208409247653, 0.208687532816, 0.208965532363, 
0.209243246671, 0.209520676117, 0.209797821075, 0.210074681919, 
0.210351259021, 0.210627552752, 0.21090356348, 0.211179291575, 
0.211454737402, 0.211729901327, 0.212004783714, 0.212279384926, 
0.212553705325, 0.21282774527, 0.213101505121, 0.213374985234, 
0.213648185967, 0.213921107674, 0.214193750709, 0.214466115425, 
0.214738202173, 0.215010011303, 0.215281543164, 0.215552798104, 
0.215823776468, 0.216094478602, 0.21636490485, 0.216635055555, 
0.216904931057, 0.217174531699, 0.217443857818, 0.217712909752, 
0.21798168784, 0.218250192415, 0.218518423813, 0.218786382367, 
0.219054068409, 0.21932148227, 0.21958862428, 0.219855494768, 
0.220122094062, 0.220388422488, 0.220654480371, 0.220920268035, 
0.221185785805, 0.221451034002, 0.221716012947, 0.22198072296, 
0.222245164359, 0.222509337463, 0.222773242589, 0.223036880051, 
0.223300250165, 0.223563353244, 0.2238261896, 0.224088759545, 
0.224351063389, 0.224613101442, 0.224874874012, 0.225136381406, 
0.22539762393, 0.22565860189, 0.22591931559, 0.226179765333, 
0.226439951422, 0.226699874157, 0.22695953384, 0.227218930768, 
0.227478065241, 0.227736937556, 0.227995548009, 0.228253896895, 
0.22851198451, 0.228769811145, 0.229027377095, 0.22928468265, 
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0.246185671353, 0.245945436553, 0.24570495918, 0.245464238999, 
0.245223275772, 0.244982069261, 0.244740619229, 0.244498925435, 
0.244256987642, 0.244014805607, 0.24377237909, 0.243529707849, 
0.243286791641, 0.243043630222, 0.24280022335, 0.242556570778, 
0.242312672262, 0.242068527555, 0.241824136409, 0.241579498578, 
0.241334613813, 0.241089481863, 0.240844102481, 0.240598475413, 
0.240352600409, 0.240106477217, 0.239860105583, 0.239613485254, 
0.239366615975, 0.23911949749, 0.238872129544, 0.238624511878, 
0.238376644236, 0.238128526359, 0.237880157987, 0.237631538861, 
0.237382668719, 0.2371335473, 0.23688417434, 0.236634549577, 
0.236384672746, 0.236134543582, 0.23588416182, 0.235633527192, 
0.235382639431, 0.235131498268, 0.234880103436, 0.234628454662, 
0.234376551677, 0.234124394209, 0.233871981984, 0.233619314731, 
0.233366392173, 0.233113214036, 0.232859780045, 0.232606089921, 
0.232352143387, 0.232097940164, 0.231843479974, 0.231588762534, 
0.231333787564, 0.231078554782, 0.230823063904, 0.230567314646, 
0.230311306723, 0.23005503985, 0.229798513738, 0.229541728101, 
0.22928468265, 0.229027377095, 0.228769811145, 0.22851198451, 
0.228253896895, 0.227995548009, 0.227736937556, 0.227478065241, 
0.227218930768, 0.22695953384, 0.226699874157, 0.226439951422, 
0.226179765333, 0.22591931559, 0.22565860189, 0.22539762393, 
0.225136381406, 0.224874874012, 0.224613101442, 0.224351063389, 
0.224088759545, 0.2238261896, 0.223563353244, 0.223300250165, 
0.223036880051, 0.222773242589, 0.222509337463, 0.222245164359, 
0.22198072296, 0.221716012947, 0.221451034002, 0.221185785805, 
0.220920268035, 0.220654480371, 0.220388422488, 0.220122094062, 
0.219855494768, 0.21958862428, 0.21932148227, 0.219054068409, 
0.218786382367, 0.218518423813, 0.218250192415, 0.21798168784, 
0.217712909752, 0.217443857818, 0.217174531699, 0.216904931057, 
0.216635055555, 0.21636490485, 0.216094478602, 0.215823776468, 
0.215552798104, 0.215281543164, 0.215010011303, 0.214738202173, 
0.214466115425, 0.214193750709, 0.213921107674, 0.213648185967, 
0.213374985234, 0.213101505121, 0.21282774527, 0.212553705325, 
0.212279384926, 0.212004783714, 0.211729901327, 0.211454737402, 
0.211179291575, 0.21090356348, 0.210627552752, 0.210351259021, 
0.210074681919, 0.209797821075, 0.209520676117, 0.209243246671, 
0.208965532363, 0.208687532816, 0.208409247653, 0.208130676495, 
0.207851818961, 0.20757267467, 0.207293243239, 0.207013524284, 
0.206733517417, 0.206453222252, 0.2061726384, 0.205891765471, 
0.205610603072, 0.205329150811, 0.205047408293, 0.204765375121, 
0.204483050898, 0.204200435225, 0.203917527701, 0.203634327924, 
0.20335083549, 0.203067049994, 0.202782971029, 0.202498598186, 
0.202213931056, 0.201928969228, 0.201643712287, 0.20135815982, 
0.20107231141, 0.20078616664, 0.200499725089, 0.200212986337, 
0.199925949961, 0.199638615537, 0.199350982639, 0.199063050838, 
0.198774819706, 0.198486288812, 0.198197457722, 0.197908326003, 
0.197618893218, 0.197329158929, 0.197039122697, 0.196748784081, 
0.196458142637, 0.196167197921, 0.195875949485, 0.195584396882, 
0.195292539661, 0.19500037737, 0.194707909556, 0.194415135763, 
0.194122055533, 0.193828668408, 0.193534973925, 0.193240971621, 
0.192946661033, 0.192652041693, 0.192357113132, 0.192061874879, 
0.191766326463, 0.191470467408, 0.191174297238, 0.190877815475, 
0.190581021638, 0.190283915244, 0.189986495811, 0.18968876285, 
0.189390715873, 0.189092354391, 0.188793677911, 0.188494685937, 
0.188195377973, 0.187895753521, 0.18759581208, 0.187295553146, 
0.186994976215, 0.186694080779, 0.186392866329, 0.186091332353, 
0.185789478338, 0.185487303768, 0.185184808123, 0.184881990885, 
0.18457885153, 0.184275389534, 0.183971604368, 0.183667495505, 
0.183363062412, 0.183058304554, 0.182753221396, 0.182447812399, 
0.182142077022, 0.18183601472, 0.181529624949, 0.18122290716, 
0.180915860803, 0.180608485323, 0.180300780166, 0.179992744774, 
0.179684378585, 0.179375681037, 0.179066651564, 0.178757289598, 
0.178447594568, 0.178137565902, 0.177827203022, 0.177516505351, 
0.177205472308, 0.176894103309, 0.176582397766, 0.176270355092, 
0.175957974695, 0.175645255979, 0.175332198348, 0.175018801202, 
0.174705063937, 0.174390985949, 0.174076566628, 0.173761805364, 
0.173446701542, 0.173131254545, 0.172815463755, 0.172499328546, 
0.172182848295, 0.171866022373, 0.171548850146, 0.171231330982, 
0.170913464242, 0.170595249286, 0.170276685469, 0.169957772145, 
0.169638508664, 0.169318894373, 0.168998928615, 0.168678610731, 
0.168357940058, 0.16803691593, 0.167715537679, 0.167393804631, 
0.167071716111, 0.16674927144, 0.166426469936, 0.166103310913, 
0.165779793681, 0.165455917548, 0.165131681818, 0.164807085792, 
0.164482128766, 0.164156810034, 0.163831128886, 0.163505084608, 
0.163178676483, 0.162851903789, 0.162524765803, 0.162197261796, 
0.161869391036, 0.161541152788, 0.161212546311, 0.160883570863, 
0.160554225695, 0.160224510058, 0.159894423197, 0.159563964351, 
0.159233132759, 0.158901927654, 0.158570348265, 0.158238393817, 
0.15790606353, 0.157573356623, 0.157240272307, 0.156906809791, 
0.156572968279, 0.156238746972, 0.155904145066, 0.155569161751, 
0.155233796214, 0.15489804764, 0.154561915205, 0.154225398084, 
0.153888495445, 0.153551206454, 0.153213530271, 0.152875466051, 
0.152537012946, 0.152198170101, 0.151858936658, 0.151519311753, 
0.151179294519, 0.150838884082, 0.150498079565, 0.150156880085, 
0.149815284753, 0.149473292678, 0.149130902961, 0.148788114699, 
0.148444926984, 0.148101338903, 0.147757349537, 0.147412957962, 
0.147068163249, 0.146722964463, 0.146377360665, 0.146031350908, 
0.145684934242, 0.14533810971, 0.144990876349, 0.144643233193, 
0.144295179266, 0.14394671359, 0.143597835179, 0.143248543043, 
0.142898836183, 0.142548713597, 0.142198174276, 0.141847217205, 
0.141495841361, 0.141144045718, 0.140791829241, 0.14043919089, 
0.140086129618, 0.139732644373, 0.139378734095, 0.139024397717, 
0.138669634167, 0.138314442365, 0.137958821225, 0.137602769653, 
0.137246286551, 0.13688937081, 0.136532021316, 0.13617423695, 
0.135816016581, 0.135457359075, 0.13509826329, 0.134738728074, 
0.13437875227, 0.134018334713, 0.13365747423, 0.133296169642, 
0.132934419758, 0.132572223385, 0.132209579317, 0.131846486342, 
0.131482943242, 0.131118948787, 0.130754501741, 0.13038960086, 
0.130024244891, 0.129658432571, 0.129292162631, 0.128925433793, 
0.128558244767, 0.128190594259, 0.127822480963, 0.127453903564, 
0.127084860738, 0.126715351154, 0.126345373469, 0.125974926331, 
0.12560400838, 0.125232618245, 0.124860754545, 0.12448841589, 
0.124115600881, 0.123742308106, 0.123368536146, 0.12299428357, 
0.122619548937, 0.122244330795, 0.121868627682, 0.121492438126, 
0.121115760642, 0.120738593735, 0.120360935901, 0.119982785621, 
0.119604141367, 0.1192250016, 0.118845364768, 0.118465229306, 
0.118084593641, 0.117703456185, 0.117321815339, 0.11693966949, 
0.116557017014, 0.116173856276, 0.115790185624, 0.115406003396, 
0.115021307918, 0.1146360975, 0.11425037044, 0.113864125022, 
0.113477359516, 0.113090072181, 0.112702261257, 0.112313924974, 
0.111925061545, 0.111535669171, 0.111145746034, 0.110755290307, 
0.110364300142, 0.109972773679, 0.109580709043, 0.10918810434, 
0.108794957663, 0.108401267088, 0.108007030675, 0.107612246467, 
0.10721691249, 0.106821026753, 0.106424587249, 0.106027591953, 
0.10563003882, 0.105231925791, 0.104833250787, 0.10443401171, 
0.104034206444, 0.103633832853, 0.103232888785, 0.102831372066, 
0.102429280502, 0.102026611881, 0.101623363968, 0.10121953451, 
0.100815121233, 0.100410121841, 0.100004534016, 0.0995983554201, 
0.0991915836918, 0.098784216448, 0.098376251283, 0.0979676857678, 
0.0975585174503, 0.0971487438546, 0.0967383624809, 0.0963273708049, 
0.0959157662776, 0.095503546325, 0.0950907083474, 0.0946772497194, 
0.0942631677893, 0.0938484598786, 0.0934331232819, 0.0930171552661, 
0.0926005530704, 0.0921833139053, 0.0917654349529, 0.0913469133655, 
0.0909277462662, 0.0905079307475, 0.0900874638713, 0.0896663426683, 
0.0892445641375, 0.0888221252457, 0.0883990229268, 0.0879752540816, 
0.0875508155769, 0.0871257042449, 0.0866999168832, 0.0862734502535, 
0.0858463010813, 0.0854184660553, 0.0849899418268, 0.084560725009, 
0.0841308121761, 0.0837001998631, 0.0832688845646, 0.0828368627345, 
0.082404130785, 0.0819706850859, 0.081536521964, 0.081101637702, 
0.080666028538, 0.0802296906646, 0.0797926202279, 0.0793548133268, 
0.078916266012, 0.0784769742851, 0.0780369340979, 0.077596141351, 
0.0771545918932, 0.0767122815202, 0.076269205974, 0.0758253609412, 
0.0753807420524, 0.0749353448811, 0.074489164942, 0.0740421976905, 
0.0735944385211, 0.0731458827663, 0.0726965256949, 0.0722463625114, 
0.0717953883543, 0.0713435982942, 0.0708909873334, 0.0704375504035, 
0.0699832823643, 0.0695281780022, 0.0690722320286, 0.0686154390782, 
0.0681577937072, 0.0676992903918, 0.0672399235259, 0.0667796874201, 
0.0663185762986, 0.0658565842984, 0.0653937054663, 0.0649299337573, 
0.0644652630325, 0.0639996870564, 0.0635331994951, 0.0630657939132, 
0.0625974637723, 0.0621282024276, 0.0616580031256, 0.0611868590013, 
0.0607147630756, 0.060241708252, 0.0597676873138, 0.059292692921, 
0.058816717607, 0.0583397537752, 0.0578617936955, 0.0573828295011, 
0.0569028531841, 0.0564218565922, 0.0559398314244, 0.0554567692269, 
0.054972661389, 0.0544874991381, 0.0540012735356, 0.053513975472, 
0.0530255956613, 0.0525361246366, 0.052045552744, 0.0515538701374, 
0.0510610667724, 0.0505671324, 0.0500720565609, 0.0495758285778, 
0.0490784375496, 0.0485798723434, 0.048080121587, 0.0475791736615, 
0.0470770166928, 0.0465736385427, 0.0460690268006, 0.0455631687734, 
0.0450560514761, 0.0445476616215, 0.0440379856092, 0.0435270095144, 
0.0430147190762, 0.0425010996849, 0.0419861363691, 0.0414698137822, 
0.0409521161875, 0.0404330274434, 0.0399125309876, 0.0393906098197, 
0.0388672464844, 0.0383424230521, 0.0378161210995, 0.037288321689, 
0.0367590053466, 0.0362281520387, 0.0356957411476, 0.0351617514458, 
0.034626161068, 0.0340889474822, 0.0335500874589, 0.033009557038, 
0.032467331494, 0.0319233852988, 0.0313776920821, 0.0308302245895, 
0.0302809546372, 0.0297298530646, 0.0291768896823, 0.0286220332182, 
0.0280652512583, 0.0275065101844, 0.0269457751062, 0.02638300979, 
0.0258181765805, 0.0252512363179, 0.0246821482486, 0.0241108699283, 
0.0235373571186, 0.0229615636755, 0.0223834414285, 0.0218029400512, 
0.0212200069209, 0.0206345869682, 0.0200466225144, 0.0194560530967, 
0.0188628152806, 0.0182668424588, 0.0176680646372, 0.0170664082066, 
0.016461795704, 0.0158541455627, 0.015243371858, 0.0146293840521, 
0.0140120867521, 0.0133913794939, 0.0127671565806, 0.0121393070128, 
0.0115077145716, 0.0108722581496, 0.0102328124764, 0.00958924947315, 
0.00894144061242, 0.00828926090091, 0.00763259551896, 0.00697135089651, 
0.00630547338383, 0.00563498133279, 0.00496002177703, 0.00428097439553, 
0.00359865177269, 0.00291471045349, 0.00223256762114, 0.00155968193081, 
0.000914116389555};

static const double yu[4001]={
0.0540012735356, 0.0544874991381, 0.054972661389, 0.0554567692269, 
0.0559398314244, 0.0564218565922, 0.0569028531841, 0.0573828295011, 
0.0578617936955, 0.0583397537752, 0.058816717607, 0.059292692921, 
0.0597676873138, 0.060241708252, 0.0607147630756, 0.0611868590013, 
0.0616580031256, 0.0621282024276, 0.0625974637723, 0.0630657939132, 
0.0635331994951, 0.0639996870564, 0.0644652630325, 0.0649299337573, 
0.0653937054663, 0.0658565842984, 0.0663185762986, 0.0667796874201, 
0.0672399235259, 0.0676992903918, 0.0681577937072, 0.0686154390782, 
0.0690722320286, 0.0695281780022, 0.0699832823643, 0.0704375504035, 
0.0708909873334, 0.0713435982942, 0.0717953883543, 0.0722463625114, 
0.0726965256949, 0.0731458827663, 0.0735944385211, 0.0740421976905, 
0.074489164942, 0.0749353448811, 0.0753807420524, 0.0758253609412, 
0.076269205974, 0.0767122815202, 0.0771545918932, 0.077596141351, 
0.0780369340979, 0.0784769742851, 0.078916266012, 0.0793548133268, 
0.0797926202279, 0.0802296906646, 0.080666028538, 0.081101637702, 
0.081536521964, 0.0819706850859, 0.082404130785, 0.0828368627345, 
0.0832688845646, 0.0837001998631, 0.0841308121761, 0.084560725009, 
0.0849899418268, 0.0854184660553, 0.0858463010813, 0.0862734502535, 
0.0866999168832, 0.0871257042449, 0.0875508155769, 0.0879752540816, 
0.0883990229268, 0.0888221252457, 0.0892445641375, 0.0896663426683, 
0.0900874638713, 0.0905079307475, 0.0909277462662, 0.0913469133655, 
0.0917654349529, 0.0921833139053, 0.0926005530704, 0.0930171552661, 
0.0934331232819, 0.0938484598786, 0.0942631677893, 0.0946772497194, 
0.0950907083474, 0.095503546325, 0.0959157662776, 0.0963273708049, 
0.0967383624809, 0.0971487438546, 0.0975585174503, 0.0979676857678, 
0.098376251283, 0.098784216448, 0.0991915836918, 0.0995983554201, 
0.100004534016, 0.100410121841, 0.100815121233, 0.10121953451, 
0.101623363968, 0.102026611881, 0.102429280502, 0.102831372066, 
0.103232888785, 0.103633832853, 0.104034206444, 0.10443401171, 
0.104833250787, 0.105231925791, 0.10563003882, 0.106027591953, 
0.106424587249, 0.106821026753, 0.10721691249, 0.107612246467, 
0.108007030675, 0.108401267088, 0.108794957663, 0.10918810434, 
0.109580709043, 0.109972773679, 0.110364300142, 0.110755290307, 
0.111145746034, 0.111535669171, 0.111925061545, 0.112313924974, 
0.112702261257, 0.113090072181, 0.113477359516, 0.113864125022, 
0.11425037044, 0.1146360975, 0.115021307918, 0.115406003396, 
0.115790185624, 0.116173856276, 0.116557017014, 0.11693966949, 
0.117321815339, 0.117703456185, 0.118084593641, 0.118465229306, 
0.118845364768, 0.1192250016, 0.119604141367, 0.119982785621, 
0.120360935901, 0.120738593735, 0.121115760642, 0.121492438126, 
0.121868627682, 0.122244330795, 0.122619548937, 0.12299428357, 
0.123368536146, 0.123742308106, 0.124115600881, 0.12448841589, 
0.124860754545, 0.125232618245, 0.12560400838, 0.125974926331, 
0.126345373469, 0.126715351154, 0.127084860738, 0.127453903564, 
0.127822480963, 0.128190594259, 0.128558244767, 0.128925433793, 
0.129292162631, 0.129658432571, 0.130024244891, 0.13038960086, 
0.130754501741, 0.131118948787, 0.131482943242, 0.131846486342, 
0.132209579317, 0.132572223385, 0.132934419758, 0.133296169642, 
0.13365747423, 0.134018334713, 0.13437875227, 0.134738728074, 
0.13509826329, 0.135457359075, 0.135816016581, 0.13617423695, 
0.136532021316, 0.13688937081, 0.137246286551, 0.137602769653, 
0.137958821225, 0.138314442365, 0.138669634167, 0.139024397717, 
0.139378734095, 0.139732644373, 0.140086129618, 0.14043919089, 
0.140791829241, 0.141144045718, 0.141495841361, 0.141847217205, 
0.142198174276, 0.142548713597, 0.142898836183, 0.143248543043, 
0.143597835179, 0.14394671359, 0.144295179266, 0.144643233193, 
0.144990876349, 0.14533810971, 0.145684934242, 0.146031350908, 
0.146377360665, 0.146722964463, 0.147068163249, 0.147412957962, 
0.147757349537, 0.148101338903, 0.148444926984, 0.148788114699, 
0.149130902961, 0.149473292678, 0.149815284753, 0.150156880085, 
0.150498079565, 0.150838884082, 0.151179294519, 0.151519311753, 
0.151858936658, 0.152198170101, 0.152537012946, 0.152875466051, 
0.153213530271, 0.153551206454, 0.153888495445, 0.154225398084, 
0.154561915205, 0.15489804764, 0.155233796214, 0.155569161751, 
0.155904145066, 0.156238746972, 0.156572968279, 0.156906809791, 
0.157240272307, 0.157573356623, 0.15790606353, 0.158238393817, 
0.158570348265, 0.158901927654, 0.159233132759, 0.159563964351, 
0.159894423197, 0.160224510058, 0.160554225695, 0.160883570863, 
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0.295978486277, 0.295789529101, 0.295600370069, 0.295411009053, 
0.295221445924, 0.295031680553, 0.294841712811, 0.294651542566, 
0.29446116969, 0.294270594051, 0.294079815519, 0.293888833963, 
0.293697649251, 0.293506261251, 0.293314669832, 0.29312287486, 
0.292930876204, 0.292738673731, 0.292546267306, 0.292353656796, 
0.292160842068, 0.291967822987, 0.291774599419, 0.291581171228, 
0.29138753828, 0.291193700439, 0.290999657568, 0.290805409533, 
0.290610956195, 0.290416297419, 0.290221433068, 0.290026363003, 
0.289831087087, 0.289635605182, 0.289439917148, 0.289244022849, 
0.289047922144, 0.288851614893, 0.288655100957, 0.288458380196, 
0.28826145247, 0.288064317636, 0.287866975555, 0.287669426085, 
0.287471669084, 0.287273704409, 0.287075531918, 0.286877151468, 
0.286678562916, 0.286479766119, 0.286280760932, 0.286081547211, 
0.285882124811, 0.285682493588, 0.285482653395, 0.285282604088, 
0.285082345521, 0.284881877546, 0.284681200017, 0.284480312788, 
0.284279215709, 0.284077908635, 0.283876391415, 0.283674663903, 
0.283472725948, 0.283270577402, 0.283068218114, 0.282865647935, 
0.282662866715, 0.282459874302, 0.282256670545, 0.282053255293, 
0.281849628394, 0.281645789695, 0.281441739045, 0.281237476289, 
0.281033001275, 0.280828313848, 0.280623413854, 0.280418301139, 
0.280212975549, 0.280007436926, 0.279801685116, 0.279595719963, 
0.27938954131, 0.279183149, 0.278976542875, 0.278769722779, 
0.278562688553, 0.278355440038, 0.278147977076, 0.277940299507, 
0.277732407172, 0.27752429991, 0.277315977561, 0.277107439965, 
0.276898686958, 0.276689718381, 0.276480534071, 0.276271133865, 
0.2760615176, 0.275851685114, 0.275641636241, 0.275431370818, 
0.275220888681, 0.275010189664, 0.274799273601, 0.274588140328, 
0.274376789677, 0.274165221481, 0.273953435575, 0.273741431789, 
0.273529209956, 0.273316769908, 0.273104111476, 0.272891234489, 
0.272678138779, 0.272464824175, 0.272251290507, 0.272037537604, 
0.271823565293, 0.271609373403, 0.271394961762, 0.271180330196, 
0.270965478533, 0.270750406598, 0.270535114218, 0.270319601217, 
0.270103867421, 0.269887912653, 0.269671736739, 0.2694553395, 
0.269238720761, 0.269021880344, 0.268804818071, 0.268587533763, 
0.268370027242, 0.268152298328, 0.267934346842, 0.267716172603, 
0.26749777543, 0.267279155143, 0.26706031156, 0.266841244498, 
0.266621953774, 0.266402439207, 0.266182700611, 0.265962737803, 
0.265742550598, 0.265522138811, 0.265301502256, 0.265080640748, 
0.2648595541, 0.264638242124, 0.264416704633, 0.264194941439, 
0.263972952353, 0.263750737186, 0.263528295749, 0.263305627851, 
0.263082733302, 0.26285961191, 0.262636263484, 0.262412687831, 
0.26218888476, 0.261964854076, 0.261740595585, 0.261516109095, 
0.261291394408, 0.261066451331, 0.260841279668, 0.260615879221, 
0.260390249794, 0.260164391189, 0.259938303209, 0.259711985655, 
0.259485438327, 0.259258661026, 0.259031653551, 0.258804415703, 
0.258576947278, 0.258349248077, 0.258121317895, 0.25789315653, 
0.257664763779, 0.257436139437, 0.2572072833, 0.256978195162, 
0.256748874817, 0.256519322059, 0.256289536681, 0.256059518475, 
0.255829267233, 0.255598782747, 0.255368064807, 0.255137113202, 
0.254905927723, 0.254674508159, 0.254442854297, 0.254210965925, 
0.253978842831, 0.253746484801, 0.253513891621, 0.253281063075, 
0.253047998949, 0.252814699027, 0.252581163092, 0.252347390927, 
0.252113382314, 0.251879137035, 0.251644654871, 0.251409935601, 
0.251174979007, 0.250939784865, 0.250704352956, 0.250468683057, 
0.250232774945, 0.249996628397, 0.249760243188, 0.249523619094, 
0.249286755888, 0.249049653346, 0.24881231124, 0.248574729343, 
0.248336907427, 0.248098845263, 0.247860542621, 0.247621999273, 
0.247383214985, 0.247144189529, 0.24690492267, 0.246665414177, 
0.246425663816, 0.246185671353, 0.245945436553, 0.24570495918, 
0.245464238999, 0.245223275772, 0.244982069261, 0.244740619229, 
0.244498925435, 0.244256987642, 0.244014805607, 0.24377237909, 
0.243529707849, 0.243286791641, 0.243043630222, 0.24280022335, 
0.242556570778, 0.242312672262, 0.242068527555, 0.241824136409, 
0.241579498578, 0.241334613813, 0.241089481863, 0.240844102481, 
0.240598475413, 0.240352600409, 0.240106477217, 0.239860105583, 
0.239613485254, 0.239366615975, 0.23911949749, 0.238872129544, 
0.238624511878, 0.238376644236, 0.238128526359, 0.237880157987, 
0.237631538861, 0.237382668719, 0.2371335473, 0.23688417434, 
0.236634549577, 0.236384672746, 0.236134543582, 0.23588416182, 
0.235633527192, 0.235382639431, 0.235131498268, 0.234880103436, 
0.234628454662, 0.234376551677, 0.234124394209, 0.233871981984, 
0.233619314731, 0.233366392173, 0.233113214036, 0.232859780045, 
0.232606089921, 0.232352143387, 0.232097940164, 0.231843479974, 
0.231588762534, 0.231333787564, 0.231078554782, 0.230823063904, 
0.230567314646, 0.230311306723, 0.23005503985, 0.229798513738, 
0.229541728101, 0.22928468265, 0.229027377095, 0.228769811145, 
0.22851198451, 0.228253896895, 0.227995548009, 0.227736937556, 
0.227478065241, 0.227218930768, 0.22695953384, 0.226699874157, 
0.226439951422, 0.226179765333, 0.22591931559, 0.22565860189, 
0.22539762393, 0.225136381406, 0.224874874012, 0.224613101442, 
0.224351063389, 0.224088759545, 0.2238261896, 0.223563353244, 
0.223300250165, 0.223036880051, 0.222773242589, 0.222509337463, 
0.222245164359, 0.22198072296, 0.221716012947, 0.221451034002, 
0.221185785805, 0.220920268035, 0.220654480371, 0.220388422488, 
0.220122094062, 0.219855494768, 0.21958862428, 0.21932148227, 
0.219054068409, 0.218786382367, 0.218518423813, 0.218250192415, 
0.21798168784, 0.217712909752, 0.217443857818, 0.217174531699, 
0.216904931057, 0.216635055555, 0.21636490485, 0.216094478602, 
0.215823776468, 0.215552798104, 0.215281543164, 0.215010011303, 
0.214738202173, 0.214466115425, 0.214193750709, 0.213921107674, 
0.213648185967, 0.213374985234, 0.213101505121, 0.21282774527, 
0.212553705325, 0.212279384926, 0.212004783714, 0.211729901327, 
0.211454737402, 0.211179291575, 0.21090356348, 0.210627552752, 
0.210351259021, 0.210074681919, 0.209797821075, 0.209520676117, 
0.209243246671, 0.208965532363, 0.208687532816, 0.208409247653, 
0.208130676495, 0.207851818961, 0.20757267467, 0.207293243239, 
0.207013524284, 0.206733517417, 0.206453222252, 0.2061726384, 
0.205891765471, 0.205610603072, 0.205329150811, 0.205047408293, 
0.204765375121, 0.204483050898, 0.204200435225, 0.203917527701, 
0.203634327924, 0.20335083549, 0.203067049994, 0.202782971029, 
0.202498598186, 0.202213931056, 0.201928969228, 0.201643712287, 
0.20135815982, 0.20107231141, 0.20078616664, 0.200499725089, 
0.200212986337, 0.199925949961, 0.199638615537, 0.199350982639, 
0.199063050838, 0.198774819706, 0.198486288812, 0.198197457722, 
0.197908326003, 0.197618893218, 0.197329158929, 0.197039122697, 
0.196748784081, 0.196458142637, 0.196167197921, 0.195875949485, 
0.195584396882, 0.195292539661, 0.19500037737, 0.194707909556, 
0.194415135763, 0.194122055533, 0.193828668408, 0.193534973925, 
0.193240971621, 0.192946661033, 0.192652041693, 0.192357113132, 
0.192061874879, 0.191766326463, 0.191470467408, 0.191174297238, 
0.190877815475, 0.190581021638, 0.190283915244, 0.189986495811, 
0.18968876285, 0.189390715873, 0.189092354391, 0.188793677911, 
0.188494685937, 0.188195377973, 0.187895753521, 0.18759581208, 
0.187295553146, 0.186994976215, 0.186694080779, 0.186392866329, 
0.186091332353, 0.185789478338, 0.185487303768, 0.185184808123, 
0.184881990885, 0.18457885153, 0.184275389534, 0.183971604368, 
0.183667495505, 0.183363062412, 0.183058304554, 0.182753221396, 
0.182447812399, 0.182142077022, 0.18183601472, 0.181529624949, 
0.18122290716, 0.180915860803, 0.180608485323, 0.180300780166, 
0.179992744774, 0.179684378585, 0.179375681037, 0.179066651564, 
0.178757289598, 0.178447594568, 0.178137565902, 0.177827203022, 
0.177516505351, 0.177205472308, 0.176894103309, 0.176582397766, 
0.176270355092, 0.175957974695, 0.175645255979, 0.175332198348, 
0.175018801202, 0.174705063937, 0.174390985949, 0.174076566628, 
0.173761805364, 0.173446701542, 0.173131254545, 0.172815463755, 
0.172499328546, 0.172182848295, 0.171866022373, 0.171548850146, 
0.171231330982, 0.170913464242, 0.170595249286, 0.170276685469, 
0.169957772145, 0.169638508664, 0.169318894373, 0.168998928615, 
0.168678610731, 0.168357940058, 0.16803691593, 0.167715537679, 
0.167393804631, 0.167071716111, 0.16674927144, 0.166426469936, 
0.166103310913, 0.165779793681, 0.165455917548, 0.165131681818, 
0.164807085792, 0.164482128766, 0.164156810034, 0.163831128886, 
0.163505084608, 0.163178676483, 0.162851903789, 0.162524765803, 
0.162197261796, 0.161869391036, 0.161541152788, 0.161212546311, 
0.160883570863, 0.160554225695, 0.160224510058, 0.159894423197, 
0.159563964351, 0.159233132759, 0.158901927654, 0.158570348265, 
0.158238393817, 0.15790606353, 0.157573356623, 0.157240272307, 
0.156906809791, 0.156572968279, 0.156238746972, 0.155904145066, 
0.155569161751, 0.155233796214, 0.15489804764, 0.154561915205, 
0.154225398084, 0.153888495445, 0.153551206454, 0.153213530271, 
0.152875466051, 0.152537012946, 0.152198170101, 0.151858936658, 
0.151519311753, 0.151179294519, 0.150838884082, 0.150498079565, 
0.150156880085, 0.149815284753, 0.149473292678, 0.149130902961, 
0.148788114699, 0.148444926984, 0.148101338903, 0.147757349537, 
0.147412957962, 0.147068163249, 0.146722964463, 0.146377360665, 
0.146031350908, 0.145684934242, 0.14533810971, 0.144990876349, 
0.144643233193, 0.144295179266, 0.14394671359, 0.143597835179, 
0.143248543043, 0.142898836183, 0.142548713597, 0.142198174276, 
0.141847217205, 0.141495841361, 0.141144045718, 0.140791829241, 
0.14043919089, 0.140086129618, 0.139732644373, 0.139378734095, 
0.139024397717, 0.138669634167, 0.138314442365, 0.137958821225, 
0.137602769653, 0.137246286551, 0.13688937081, 0.136532021316, 
0.13617423695, 0.135816016581, 0.135457359075, 0.13509826329, 
0.134738728074, 0.13437875227, 0.134018334713, 0.13365747423, 
0.133296169642, 0.132934419758, 0.132572223385, 0.132209579317, 
0.131846486342, 0.131482943242, 0.131118948787, 0.130754501741, 
0.13038960086, 0.130024244891, 0.129658432571, 0.129292162631, 
0.128925433793, 0.128558244767, 0.128190594259, 0.127822480963, 
0.127453903564, 0.127084860738, 0.126715351154, 0.126345373469, 
0.125974926331, 0.12560400838, 0.125232618245, 0.124860754545, 
0.12448841589, 0.124115600881, 0.123742308106, 0.123368536146, 
0.12299428357, 0.122619548937, 0.122244330795, 0.121868627682, 
0.121492438126, 0.121115760642, 0.120738593735, 0.120360935901, 
0.119982785621, 0.119604141367, 0.1192250016, 0.118845364768, 
0.118465229306, 0.118084593641, 0.117703456185, 0.117321815339, 
0.11693966949, 0.116557017014, 0.116173856276, 0.115790185624, 
0.115406003396, 0.115021307918, 0.1146360975, 0.11425037044, 
0.113864125022, 0.113477359516, 0.113090072181, 0.112702261257, 
0.112313924974, 0.111925061545, 0.111535669171, 0.111145746034, 
0.110755290307, 0.110364300142, 0.109972773679, 0.109580709043, 
0.10918810434, 0.108794957663, 0.108401267088, 0.108007030675, 
0.107612246467, 0.10721691249, 0.106821026753, 0.106424587249, 
0.106027591953, 0.10563003882, 0.105231925791, 0.104833250787, 
0.10443401171, 0.104034206444, 0.103633832853, 0.103232888785, 
0.102831372066, 0.102429280502, 0.102026611881, 0.101623363968, 
0.10121953451, 0.100815121233, 0.100410121841, 0.100004534016, 
0.0995983554201, 0.0991915836918, 0.098784216448, 0.098376251283, 
0.0979676857678, 0.0975585174503, 0.0971487438546, 0.0967383624809, 
0.0963273708049, 0.0959157662776, 0.095503546325, 0.0950907083474, 
0.0946772497194, 0.0942631677893, 0.0938484598786, 0.0934331232819, 
0.0930171552661, 0.0926005530704, 0.0921833139053, 0.0917654349529, 
0.0913469133655, 0.0909277462662, 0.0905079307475, 0.0900874638713, 
0.0896663426683, 0.0892445641375, 0.0888221252457, 0.0883990229268, 
0.0879752540816, 0.0875508155769, 0.0871257042449, 0.0866999168832, 
0.0862734502535, 0.0858463010813, 0.0854184660553, 0.0849899418268, 
0.084560725009, 0.0841308121761, 0.0837001998631, 0.0832688845646, 
0.0828368627345, 0.082404130785, 0.0819706850859, 0.081536521964, 
0.081101637702, 0.080666028538, 0.0802296906646, 0.0797926202279, 
0.0793548133268, 0.078916266012, 0.0784769742851, 0.0780369340979, 
0.077596141351, 0.0771545918932, 0.0767122815202, 0.076269205974, 
0.0758253609412, 0.0753807420524, 0.0749353448811, 0.074489164942, 
0.0740421976905, 0.0735944385211, 0.0731458827663, 0.0726965256949, 
0.0722463625114, 0.0717953883543, 0.0713435982942, 0.0708909873334, 
0.0704375504035, 0.0699832823643, 0.0695281780022, 0.0690722320286, 
0.0686154390782, 0.0681577937072, 0.0676992903918, 0.0672399235259, 
0.0667796874201, 0.0663185762986, 0.0658565842984, 0.0653937054663, 
0.0649299337573, 0.0644652630325, 0.0639996870564, 0.0635331994951, 
0.0630657939132, 0.0625974637723, 0.0621282024276, 0.0616580031256, 
0.0611868590013, 0.0607147630756, 0.060241708252, 0.0597676873138, 
0.059292692921, 0.058816717607, 0.0583397537752, 0.0578617936955, 
0.0573828295011, 0.0569028531841, 0.0564218565922, 0.0559398314244, 
0.0554567692269, 0.054972661389, 0.0544874991381, 0.0540012735356, 
0.053513975472, 0.0530255956613, 0.0525361246366, 0.052045552744, 
0.0515538701374, 0.0510610667724, 0.0505671324, 0.0500720565609, 
0.0495758285778, 0.0490784375496, 0.0485798723434, 0.048080121587, 
0.0475791736615, 0.0470770166928, 0.0465736385427, 0.0460690268006, 
0.0455631687734, 0.0450560514761, 0.0445476616215, 0.0440379856092, 
0.0435270095144, 0.0430147190762, 0.0425010996849, 0.0419861363691, 
0.0414698137822, 0.0409521161875, 0.0404330274434, 0.0399125309876, 
0.0393906098197, 0.0388672464844, 0.0383424230521, 0.0378161210995, 
0.037288321689, 0.0367590053466, 0.0362281520387, 0.0356957411476, 
0.0351617514458, 0.034626161068, 0.0340889474822, 0.0335500874589, 
0.033009557038, 0.032467331494, 0.0319233852988, 0.0313776920821, 
0.0308302245895, 0.0302809546372, 0.0297298530646, 0.0291768896823, 
0.0286220332182, 0.0280652512583, 0.0275065101844, 0.0269457751062, 
0.02638300979, 0.0258181765805, 0.0252512363179, 0.0246821482486, 
0.0241108699283, 0.0235373571186, 0.0229615636755, 0.0223834414285, 
0.0218029400512, 0.0212200069209, 0.0206345869682, 0.0200466225144, 
0.0194560530967, 0.0188628152806, 0.0182668424588, 0.0176680646372, 
0.0170664082066, 0.016461795704, 0.0158541455627, 0.015243371858, 
0.0146293840521, 0.0140120867521, 0.0133913794939, 0.0127671565806, 
0.0121393070128, 0.0115077145716, 0.0108722581496, 0.0102328124764, 
0.00958924947315, 0.00894144061242, 0.00828926090091, 0.00763259551896, 
0.00697135089651, 0.00630547338383, 0.00563498133279, 0.00496002177703, 
0.00428097439553, 0.00359865177269, 0.00291471045349, 0.00223256762114, 
0.00155968193081};

static const double d[4001]={
0.00452748488962, 0.00448708334609, 0.00444748250813, 0.00440865837229, 
0.00437058789287, 0.00433324893436, 0.00429662022678, 0.00426068132363, 
0.0042254125622, 0.00419079502623, 0.00415681051068, 0.00412344148845, 
0.00409067107899, 0.00405848301861, 0.00402686163245, 0.00399579180797, 
0.00396525896978, 0.00393524905597, 0.00390574849553, 0.00387674418701, 
0.00384822347837, 0.00382017414768, 0.00379258438501, 0.00376544277508, 
0.00373873828084, 0.00371246022789, 0.00368659828962, 0.00366114247308, 
0.00363608310557, 0.00361141082185, 0.00358711655197, 0.00356319150963, 
0.00353962718117, 0.00351641531502, 0.00349354791163, 0.00347101721386, 
0.00344881569787, 0.00342693606432, 0.00340537123006, 0.00338411432013, 
0.00336315866014, 0.00334249776893, 0.00332212535166, 0.0033020352931, 
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0.00127297492075, 0.00127493681744, 0.00127690684241, 0.00127888504619, 
0.00128087147972, 0.0012828661944, 0.00128486924204, 0.00128688067491, 
0.00128890054571, 0.0012909289076, 0.00129296581419, 0.00129501131954, 
0.0012970654782, 0.00129912834516, 0.0013011999759, 0.00130328042637, 
0.00130536975302, 0.00130746801279, 0.00130957526308, 0.00131169156185, 
0.00131381696751, 0.00131595153902, 0.00131809533583, 0.00132024841795, 
0.00132241084587, 0.00132458268066, 0.0013267639839, 0.00132895481774, 
0.00133115524486, 0.00133336532853, 0.00133558513255, 0.00133781472132, 
0.0013400541598, 0.00134230351356, 0.00134456284872, 0.00134683223204, 
0.00134911173087, 0.00135140141316, 0.0013537013475, 0.0013560116031, 
0.00135833224978, 0.00136066335804, 0.001363004999, 0.00136535724445, 
0.00136772016684, 0.00137009383928, 0.00137247833558, 0.00137487373021, 
0.00137728009837, 0.00137969751593, 0.00138212605949, 0.00138456580636, 
0.00138701683459, 0.00138947922296, 0.00139195305099, 0.00139443839897, 
0.00139693534794, 0.00139944397972, 0.0014019643769, 0.00140449662289, 
0.00140704080187, 0.00140959699884, 0.00141216529964, 0.00141474579092, 
0.00141733856017, 0.00141994369575, 0.00142256128685, 0.00142519142357, 
0.00142783419687, 0.00143048969861, 0.00143315802155, 0.00143583925937, 
0.00143853350669, 0.00144124085903, 0.00144396141292, 0.0014466952658, 
0.00144944251612, 0.00145220326329, 0.00145497760774, 0.00145776565091, 
0.00146056749526, 0.00146338324429, 0.00146621300256, 0.00146905687567, 
0.00147191497032, 0.00147478739431, 0.00147767425654, 0.00148057566701, 
0.00148349173689, 0.00148642257847, 0.00148936830523, 0.00149232903182, 
0.00149530487409, 0.0014982959491, 0.00150130237513, 0.00150432427171, 
0.00150736175966, 0.00151041496102, 0.00151348399917, 0.0015165689988, 
0.0015196700859, 0.00152278738783, 0.00152592103333, 0.00152907115248, 
0.00153223787681, 0.00153542133924, 0.00153862167415, 0.00154183901737, 
0.00154507350622, 0.00154832527951, 0.0015515944776, 0.00155488124236, 
0.00155818571723, 0.00156150804727, 0.0015648483791, 0.00156820686102, 
0.00157158364294, 0.00157497887647, 0.00157839271494, 0.00158182531336, 
0.00158527682853, 0.001588747419, 0.00159223724514, 0.00159574646913, 
0.001599275255, 0.00160282376868, 0.00160639217798, 0.00160998065266, 
0.00161358936444, 0.00161721848703, 0.00162086819616, 0.00162453866959, 
0.00162823008719, 0.00163194263092, 0.00163567648489, 0.00163943183538, 
0.00164320887087, 0.00164700778208, 0.00165082876201, 0.00165467200595, 
0.00165853771156, 0.00166242607884, 0.00166633731023, 0.0016702716106, 
0.00167422918731, 0.00167821025025, 0.00168221501188, 0.00168624368725, 
0.00169029649404, 0.00169437365265, 0.00169847538617, 0.00170260192048, 
0.00170675348425, 0.00171093030904, 0.00171513262928, 0.00171936068235, 
0.00172361470863, 0.00172789495155, 0.0017322016576, 0.00173653507644, 
0.0017408954609, 0.00174528306706, 0.00174969815428, 0.00175414098528, 
0.00175861182618, 0.00176311094654, 0.00176763861945, 0.00177219512157, 
0.00177678073318, 0.00178139573825, 0.00178604042452, 0.00179071508351, 
0.00179542001064, 0.00180015550527, 0.00180492187078, 0.00180971941459, 
0.0018145484483, 0.00181940928772, 0.00182430225294, 0.00182922766841, 
0.00183418586303, 0.0018391771702, 0.00184420192791, 0.00184926047883, 
0.00185435317038, 0.00185948035483, 0.00186464238933, 0.00186983963609, 
0.00187507246237, 0.00188034124065, 0.00188564634868, 0.00189098816956, 
0.0018963670919, 0.00190178350984, 0.00190723782322, 0.00191273043764, 
0.00191826176458, 0.00192383222149, 0.00192944223195, 0.0019350922257, 
0.00194078263884, 0.00194651391389, 0.00195228649995, 0.00195810085278, 
0.00196395743495, 0.00196985671598, 0.00197579917244, 0.00198178528813, 
0.00198781555415, 0.00199389046911, 0.00200001053924, 0.00200617627852, 
0.00201238820888, 0.0020186468603, 0.00202495277101, 0.00203130648763, 
0.00203770856534, 0.00204415956803, 0.00205066006854, 0.00205721064873, 
0.00206381189978, 0.00207046442227, 0.00207716882644, 0.00208392573237, 
0.00209073577016, 0.00209759958015, 0.00210451781314, 0.00211149113058, 
0.00211852020482, 0.0021256057193, 0.00213274836884, 0.00213994885979, 
0.00214720791036, 0.00215452625083, 0.00216190462379, 0.00216934378446, 
0.00217684450089, 0.00218440755428, 0.00219203373926, 0.00219972386417, 
0.00220747875136, 0.00221529923751, 0.00222318617393, 0.00223114042689, 
0.00223916287796, 0.00224725442433, 0.00225541597916, 0.00226364847199, 
0.00227195284904, 0.00228033007363, 0.00228878112656, 0.00229730700651, 
0.00230590873045, 0.00231458733409, 0.00232334387225, 0.00233217941938, 
0.00234109506999, 0.00235009193909, 0.00235917116275, 0.00236833389852, 
0.00237758132601, 0.00238691464739, 0.00239633508794, 0.00240584389659, 
0.00241544234653, 0.00242513173581, 0.00243491338791, 0.00244478865241, 
0.00245475890562, 0.00246482555125, 0.00247499002112, 0.00248525377582, 
0.00249561830553, 0.00250608513067, 0.00251665580276, 0.00252733190518, 
0.002538115054, 0.00254900689888, 0.00256000912386, 0.00257112344835, 
0.00258235162805, 0.00259369545589, 0.00260515676303, 0.00261673741993, 
0.00262843933738, 0.00264026446761, 0.00265221480542, 0.00266429238938, 
0.00267649930298, 0.00268883767598, 0.00270130968561, 0.00271391755796, 
0.00272666356937, 0.00273955004784, 0.00275257937452, 0.00276575398526, 
0.00277907637216, 0.00279254908526, 0.00280617473421, 0.00281995599006, 
0.00283389558705, 0.00284799632451, 0.00286226106887, 0.00287669275561, 
0.00289129439142, 0.00290606905637, 0.00292101990619, 0.00293615017459, 
0.00295146317571, 0.00296696230667, 0.00298265105015, 0.00299853297717, 
0.0030146117499, 0.0030308911246, 0.00304737495468, 0.00306406719386, 
0.00308097189953, 0.00309809323613, 0.00311543547875, 0.00313300301683, 
0.00315080035806, 0.00316883213239, 0.00318710309624, 0.00320561813684, 
0.00322438227682, 0.00324340067895, 0.00326267865105, 0.0032822216512, 
0.0033020352931, 0.00332212535166, 0.00334249776893, 0.00336315866014, 
0.00338411432013, 0.00340537123006, 0.00342693606432, 0.00344881569787, 
0.00347101721386, 0.00349354791163, 0.00351641531502, 0.00353962718117, 
0.00356319150963, 0.00358711655197, 0.00361141082185, 0.00363608310557, 
0.00366114247308, 0.00368659828962, 0.00371246022789, 0.00373873828084, 
0.00376544277508, 0.00379258438501, 0.00382017414768, 0.00384822347837, 
0.00387674418701, 0.00390574849553, 0.00393524905597, 0.00396525896978, 
0.00399579180797, 0.00402686163245, 0.00405848301861, 0.00409067107899, 
0.00412344148845, 0.00415681051068, 0.00419079502623, 0.0042254125622, 
0.00426068132363, 0.00429662022678, 0.00433324893436, 0.00437058789287, 
0.00440865837229, 0.00444748250813, 0.00448708334609, 0.00452748488962, 
0.00456871215035, 0.00461079120194, 0.00465374923719, 0.00469761462915, 
0.00474241699606, 0.00478818727079, 0.00483495777491, 0.00488276229788, 
0.00493163618171, 0.00498161641159, 0.00503274171296, 0.0050850526555, 
0.00513859176479, 0.00519340364212, 0.0052495350933, 0.00530703526712, 
0.00536595580454, 0.00542635099932, 0.00548827797136, 0.0055517968538, 
0.00561697099526, 0.00568386717858, 0.00575255585774, 0.00582311141476, 
0.0058956124384, 0.00597014202717, 0.00604678811881, 0.00612564384927, 
0.00620680794411, 0.00629038514603, 0.00637648668214, 0.00646523077577, 
0.00655674320748, 0.00665115793117, 0.00674861775151, 0.00684927507014, 
0.00695329270868, 0.00706084481825, 0.00717211788602, 0.00728731185134, 
0.00740664134544, 0.00753033707121, 0.00765864734157, 0.00779183979857, 
0.00793020333806, 0.0080740502696, 0.00822371874566, 0.00837957550016, 
0.00854201894354, 0.00871148266951, 0.00888843943902, 0.00907340571904, 
0.00926694686842, 0.00946968308125, 0.00968229622004, 0.00990553769834, 
0.0101402376057, 0.0103873153099, 0.0106477918232, 0.0109228042852, 
0.0112136229967, 0.0115216715463, 0.0118485507042, 0.0121960669323, 
0.0125662665875, 0.0129614771876, 0.0133843575048, 0.0138379587676, 
0.014325799957, 0.0148519611316, 0.0154212000253, 0.0160390989756, 
0.0167122517996, 0.0174485038723, 0.0182572639409, 0.0191499139537, 
0.0201403547744, 0.021245743317, 0.0224875041218, 0.0238927421485, 
0.0254962550132, 0.0273434629329, 0.029494782813, 0.032032347233, 
0.03507067046, 0.0387742418483, 0.0433878899527, 0.049292112201, 
0.0571108180903, 0.0679393187772, 0.0838813850823, 0.109510658328, 
0.156756288012};

static const double delta[4001]={
0.00456871215035, 0.00452748488962, 0.00448708334609, 0.00444748250813, 
0.00440865837229, 0.00437058789287, 0.00433324893436, 0.00429662022678, 
0.00426068132363, 0.0042254125622, 0.00419079502623, 0.00415681051068, 
0.00412344148845, 0.00409067107899, 0.00405848301861, 0.00402686163245, 
0.00399579180797, 0.00396525896978, 0.00393524905597, 0.00390574849553, 
0.00387674418701, 0.00384822347837, 0.00382017414768, 0.00379258438501, 
0.00376544277508, 0.00373873828084, 0.00371246022789, 0.00368659828962, 
0.00366114247308, 0.00363608310557, 0.00361141082185, 0.00358711655197, 
0.00356319150963, 0.00353962718117, 0.00351641531502, 0.00349354791163, 
0.00347101721386, 0.00344881569787, 0.00342693606432, 0.00340537123006, 
0.00338411432013, 0.00336315866014, 0.00334249776893, 0.00332212535166, 
0.0033020352931, 0.0032822216512, 0.00326267865105, 0.00324340067895, 
0.00322438227682, 0.00320561813684, 0.00318710309624, 0.00316883213239, 
0.00315080035806, 0.00313300301683, 0.00311543547875, 0.00309809323613, 
0.00308097189953, 0.00306406719386, 0.00304737495468, 0.0030308911246, 
0.0030146117499, 0.00299853297717, 0.00298265105015, 0.00296696230667, 
0.00295146317571, 0.00293615017459, 0.00292101990619, 0.00290606905637, 
0.00289129439142, 0.00287669275561, 0.00286226106887, 0.00284799632451, 
0.00283389558705, 0.00281995599006, 0.00280617473421, 0.00279254908526, 
0.00277907637216, 0.00276575398526, 0.00275257937452, 0.00273955004784, 
0.00272666356937, 0.00271391755796, 0.00270130968561, 0.00268883767598, 
0.00267649930298, 0.00266429238938, 0.00265221480542, 0.00264026446761, 
0.00262843933738, 0.00261673741993, 0.00260515676303, 0.00259369545589, 
0.00258235162805, 0.00257112344835, 0.00256000912386, 0.00254900689888, 
0.002538115054, 0.00252733190518, 0.00251665580276, 0.00250608513067, 
0.00249561830553, 0.00248525377582, 0.00247499002112, 0.00246482555125, 
0.00245475890562, 0.00244478865241, 0.00243491338791, 0.00242513173581, 
0.00241544234653, 0.00240584389659, 0.00239633508794, 0.00238691464739, 
0.00237758132601, 0.00236833389852, 0.00235917116275, 0.00235009193909, 
0.00234109506999, 0.00233217941938, 0.00232334387225, 0.00231458733409, 
0.00230590873045, 0.00229730700651, 0.00228878112656, 0.00228033007363, 
0.00227195284904, 0.00226364847199, 0.00225541597916, 0.00224725442433, 
0.00223916287796, 0.00223114042689, 0.00222318617393, 0.00221529923751, 
0.00220747875136, 0.00219972386417, 0.00219203373926, 0.00218440755428, 
0.00217684450089, 0.00216934378446, 0.00216190462379, 0.00215452625083, 
0.00214720791036, 0.00213994885979, 0.00213274836884, 0.0021256057193, 
0.00211852020482, 0.00211149113058, 0.00210451781314, 0.00209759958015, 
0.00209073577016, 0.00208392573237, 0.00207716882644, 0.00207046442227, 
0.00206381189978, 0.00205721064873, 0.00205066006854, 0.00204415956803, 
0.00203770856534, 0.00203130648763, 0.00202495277101, 0.0020186468603, 
0.00201238820888, 0.00200617627852, 0.00200001053924, 0.00199389046911, 
0.00198781555415, 0.00198178528813, 0.00197579917244, 0.00196985671598, 
0.00196395743495, 0.00195810085278, 0.00195228649995, 0.00194651391389, 
0.00194078263884, 0.0019350922257, 0.00192944223195, 0.00192383222149, 
0.00191826176458, 0.00191273043764, 0.00190723782322, 0.00190178350984, 
0.00189636709189, 0.00189098816956, 0.00188564634868, 0.00188034124065, 
0.00187507246237, 0.00186983963609, 0.00186464238933, 0.00185948035483, 
0.00185435317038, 0.00184926047883, 0.00184420192791, 0.0018391771702, 
0.00183418586303, 0.00182922766841, 0.00182430225294, 0.00181940928772, 
0.0018145484483, 0.00180971941459, 0.00180492187078, 0.00180015550527, 
0.00179542001064, 0.00179071508351, 0.00178604042452, 0.00178139573825, 
0.00177678073318, 0.00177219512157, 0.00176763861945, 0.00176311094654, 
0.00175861182618, 0.00175414098528, 0.00174969815428, 0.00174528306706, 
0.0017408954609, 0.00173653507644, 0.0017322016576, 0.00172789495155, 
0.00172361470863, 0.00171936068235, 0.00171513262928, 0.00171093030904, 
0.00170675348425, 0.00170260192048, 0.00169847538617, 0.00169437365265, 
0.00169029649404, 0.00168624368725, 0.00168221501188, 0.00167821025025, 
0.00167422918731, 0.0016702716106, 0.00166633731023, 0.00166242607884, 
0.00165853771156, 0.00165467200595, 0.00165082876201, 0.00164700778208, 
0.00164320887087, 0.00163943183538, 0.00163567648489, 0.00163194263092, 
0.00162823008719, 0.00162453866959, 0.00162086819616, 0.00161721848703, 
0.00161358936444, 0.00160998065266, 0.00160639217798, 0.00160282376868, 
0.001599275255, 0.00159574646913, 0.00159223724514, 0.001588747419, 
0.00158527682853, 0.00158182531336, 0.00157839271494, 0.00157497887647, 
0.00157158364294, 0.00156820686102, 0.0015648483791, 0.00156150804727, 
0.00155818571723, 0.00155488124236, 0.0015515944776, 0.00154832527951, 
0.00154507350622, 0.00154183901737, 0.00153862167415, 0.00153542133924, 
0.00153223787681, 0.00152907115248, 0.00152592103333, 0.00152278738783, 
0.0015196700859, 0.0015165689988, 0.00151348399917, 0.00151041496102, 
0.00150736175966, 0.00150432427171, 0.00150130237513, 0.0014982959491, 
0.00149530487409, 0.00149232903182, 0.00148936830523, 0.00148642257847, 
0.00148349173689, 0.00148057566701, 0.00147767425654, 0.00147478739431, 
0.00147191497032, 0.00146905687567, 0.00146621300256, 0.00146338324429, 
0.00146056749526, 0.00145776565091, 0.00145497760774, 0.00145220326329, 
0.00144944251612, 0.0014466952658, 0.00144396141292, 0.00144124085903, 
0.00143853350669, 0.00143583925937, 0.00143315802155, 0.00143048969861, 
0.00142783419687, 0.00142519142357, 0.00142256128685, 0.00141994369575, 
0.00141733856017, 0.00141474579092, 0.00141216529964, 0.00140959699884, 
0.00140704080187, 0.00140449662289, 0.0014019643769, 0.00139944397972, 
0.00139693534794, 0.00139443839897, 0.00139195305099, 0.00138947922296, 
0.00138701683459, 0.00138456580636, 0.00138212605949, 0.00137969751593, 
0.00137728009837, 0.00137487373021, 0.00137247833558, 0.00137009383928, 
0.00136772016684, 0.00136535724445, 0.001363004999, 0.00136066335804, 
0.00135833224978, 0.0013560116031, 0.0013537013475, 0.00135140141316, 
0.00134911173087, 0.00134683223204, 0.00134456284872, 0.00134230351356, 
0.0013400541598, 0.00133781472132, 0.00133558513255, 0.00133336532853, 
0.00133115524486, 0.00132895481774, 0.0013267639839, 0.00132458268066, 
0.00132241084587, 0.00132024841795, 0.00131809533583, 0.00131595153902, 
0.00131381696751, 0.00131169156185, 0.00130957526309, 0.00130746801279, 
0.00130536975302, 0.00130328042637, 0.0013011999759, 0.00129912834516, 
0.0012970654782, 0.00129501131954, 0.00129296581419, 0.0012909289076, 
0.00128890054571, 0.00128688067491, 0.00128486924204, 0.0012828661944, 
0.00128087147972, 0.00127888504619, 0.00127690684241, 0.00127493681744, 
0.00127297492075, 0.00127102110222, 0.00126907531218, 0.00126713750134, 
0.00126520762083, 0.0012632856222, 0.00126137145739, 0.00125946507871, 
0.00125756643891, 0.0012556754911, 0.00125379218876, 0.00125191648579, 
0.00125004833642, 0.0012481876953, 0.00124633451741, 0.00124448875812, 
0.00124265037314, 0.00124081931855, 0.00123899555078, 0.00123717902662, 
0.00123536970319, 0.00123356753796, 0.00123177248875, 0.0012299845137, 
0.0012282035713, 0.00122642962034, 0.00122466261998, 0.00122290252966, 
0.00122114930917, 0.0012194029186, 0.00121766331837, 0.00121593046918, 
0.00121420433208, 0.00121248486838, 0.00121077203973, 0.00120906580806, 
0.00120736613558, 0.00120567298483, 0.00120398631861, 0.00120230610001, 
0.00120063229243, 0.00119896485951, 0.00119730376521, 0.00119564897374, 
0.00119400044958, 0.0011923581575, 0.00119072206254, 0.00118909212998, 
0.00118746832538, 0.00118585061456, 0.0011842389636, 0.00118263333884, 
0.00118103370685, 0.00117944003447, 0.0011778522888, 0.00117627043715, 
0.00117469444712, 0.0011731242865, 0.00117155992336, 0.001170001326, 
0.00116844846294, 0.00116690130293, 0.00116535981499, 0.00116382396831, 
0.00116229373235, 0.00116076907678, 0.0011592499715, 0.0011577363866, 
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0.00568386717858, 0.00575255585774, 0.00582311141476, 0.0058956124384, 
0.00597014202717, 0.00604678811881, 0.00612564384927, 0.00620680794411, 
0.00629038514603, 0.00637648668214, 0.00646523077577, 0.00655674320748, 
0.00665115793117, 0.00674861775151, 0.00684927507014, 0.00695329270868, 
0.00706084481825, 0.00717211788602, 0.00728731185133, 0.00740664134544, 
0.00753033707121, 0.00765864734157, 0.00779183979857, 0.00793020333806, 
0.0080740502696, 0.00822371874566, 0.00837957550016, 0.00854201894354, 
0.00871148266951, 0.00888843943902, 0.00907340571904, 0.00926694686842, 
0.00946968308125, 0.00968229622004, 0.00990553769834, 0.0101402376057, 
0.0103873153099, 0.0106477918232, 0.0109228042852, 0.0112136229967, 
0.0115216715463, 0.0118485507042, 0.0121960669323, 0.0125662665875, 
0.0129614771876, 0.0133843575048, 0.0138379587676, 0.014325799957, 
0.0148519611316, 0.0154212000253, 0.0160390989756, 0.0167122517996, 
0.0174485038723, 0.0182572639409, 0.0191499139537, 0.0201403547744, 
0.021245743317, 0.0224875041218, 0.0238927421485, 0.0254962550132, 
0.0273434629329, 0.029494782813, 0.032032347233, 0.03507067046, 
0.0387742418483, 0.0433878899527, 0.049292112201, 0.0571108180903, 
0.0679393187772, 0.0838813850823, 0.109510658328, 0.156756288012, 
0.267460416142};

static const unsigned short int ncell[7523]={
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 
2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 
5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 
8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 
11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 
14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 
17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 
20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 
23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 
27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 30, 30, 
30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 
33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 
37, 37, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 
40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 44, 44, 44, 
44, 44, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 48, 48, 
48, 48, 48, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 52, 
52, 52, 52, 52, 53, 53, 53, 53, 53, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 56, 
56, 56, 56, 56, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 60, 
60, 60, 60, 60, 61, 61, 61, 61, 61, 62, 62, 62, 62, 63, 63, 63, 63, 63, 64, 64, 
64, 64, 64, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 67, 67, 67, 67, 68, 68, 68, 
68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 71, 71, 71, 71, 71, 72, 72, 72, 72, 
72, 73, 73, 73, 73, 74, 74, 74, 74, 74, 75, 75, 75, 75, 76, 76, 76, 76, 76, 77, 
77, 77, 77, 78, 78, 78, 78, 78, 79, 79, 79, 79, 80, 80, 80, 80, 80, 81, 81, 81, 
81, 82, 82, 82, 82, 83, 83, 83, 83, 83, 84, 84, 84, 84, 85, 85, 85, 85, 86, 86, 
86, 86, 86, 87, 87, 87, 87, 88, 88, 88, 88, 89, 89, 89, 89, 89, 90, 90, 90, 90, 
91, 91, 91, 91, 92, 92, 92, 92, 93, 93, 93, 93, 94, 94, 94, 94, 95, 95, 95, 95, 
95, 96, 96, 96, 96, 97, 97, 97, 97, 98, 98, 98, 98, 99, 99, 99, 99, 100, 100, 100, 
100, 101, 101, 101, 101, 102, 102, 102, 102, 103, 103, 103, 103, 104, 104, 104, 104, 105, 105, 105, 
105, 106, 106, 106, 106, 107, 107, 107, 107, 108, 108, 108, 108, 109, 109, 109, 109, 110, 110, 110, 
110, 111, 111, 111, 111, 112, 112, 112, 113, 113, 113, 113, 114, 114, 114, 114, 115, 115, 115, 115, 
116, 116, 116, 116, 117, 117, 117, 117, 118, 118, 118, 119, 119, 119, 119, 120, 120, 120, 120, 121, 
121, 121, 121, 122, 122, 122, 123, 123, 123, 123, 124, 124, 124, 124, 125, 125, 125, 126, 126, 126, 
126, 127, 127, 127, 127, 128, 128, 128, 129, 129, 129, 129, 130, 130, 130, 130, 131, 131, 131, 132, 
132, 132, 132, 133, 133, 133, 134, 134, 134, 134, 135, 135, 135, 136, 136, 136, 136, 137, 137, 137, 
137, 138, 138, 138, 139, 139, 139, 139, 140, 140, 140, 141, 141, 141, 141, 142, 142, 142, 143, 143, 
143, 144, 144, 144, 144, 145, 145, 145, 146, 146, 146, 146, 147, 147, 147, 148, 148, 148, 148, 149, 
149, 149, 150, 150, 150, 151, 151, 151, 151, 152, 152, 152, 153, 153, 153, 154, 154, 154, 154, 155, 
155, 155, 156, 156, 156, 157, 157, 157, 157, 158, 158, 158, 159, 159, 159, 160, 160, 160, 160, 161, 
161, 161, 162, 162, 162, 163, 163, 163, 164, 164, 164, 164, 165, 165, 165, 166, 166, 166, 167, 167, 
167, 168, 168, 168, 169, 169, 169, 169, 170, 170, 170, 171, 171, 171, 172, 172, 172, 173, 173, 173, 
174, 174, 174, 175, 175, 175, 176, 176, 176, 176, 177, 177, 177, 178, 178, 178, 179, 179, 179, 180, 
180, 180, 181, 181, 181, 182, 182, 182, 183, 183, 183, 184, 184, 184, 185, 185, 185, 186, 186, 186, 
187, 187, 187, 188, 188, 188, 189, 189, 189, 190, 190, 190, 191, 191, 191, 192, 192, 192, 193, 193, 
193, 194, 194, 194, 195, 195, 195, 196, 196, 196, 197, 197, 197, 198, 198, 198, 199, 199, 199, 200, 
200, 200, 201, 201, 201, 202, 202, 202, 203, 203, 203, 204, 204, 204, 205, 205, 206, 206, 206, 207, 
207, 207, 208, 208, 208, 209, 209, 209, 210, 210, 210, 211, 211, 211, 212, 212, 213, 213, 213, 214, 
214, 214, 215, 215, 215, 216, 216, 216, 217, 217, 217, 218, 218, 219, 219, 219, 220, 220, 220, 221, 
221, 221, 222, 222, 223, 223, 223, 224, 224, 224, 225, 225, 225, 226, 226, 227, 227, 227, 228, 228, 
228, 229, 229, 229, 230, 230, 231, 231, 231, 232, 232, 232, 233, 233, 234, 234, 234, 235, 235, 235, 
236, 236, 237, 237, 237, 238, 238, 238, 239, 239, 240, 240, 240, 241, 241, 241, 242, 242, 243, 243, 
243, 244, 244, 244, 245, 245, 246, 246, 246, 247, 247, 248, 248, 248, 249, 249, 249, 250, 250, 251, 
251, 251, 252, 252, 253, 253, 253, 254, 254, 254, 255, 255, 256, 256, 256, 257, 257, 258, 258, 258, 
259, 259, 260, 260, 260, 261, 261, 262, 262, 262, 263, 263, 264, 264, 264, 265, 265, 266, 266, 266, 
267, 267, 268, 268, 268, 269, 269, 270, 270, 270, 271, 271, 272, 272, 272, 273, 273, 274, 274, 274, 
275, 275, 276, 276, 276, 277, 277, 278, 278, 278, 279, 279, 280, 280, 280, 281, 281, 282, 282, 283, 
283, 283, 284, 284, 285, 285, 285, 286, 286, 287, 287, 288, 288, 288, 289, 289, 290, 290, 290, 291, 
291, 292, 292, 293, 293, 293, 294, 294, 295, 295, 296, 296, 296, 297, 297, 298, 298, 298, 299, 299, 
300, 300, 301, 301, 301, 302, 302, 303, 303, 304, 304, 304, 305, 305, 306, 306, 307, 307, 307, 308, 
308, 309, 309, 310, 310, 311, 311, 311, 312, 312, 313, 313, 314, 314, 314, 315, 315, 316, 316, 317, 
317, 318, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 322, 323, 323, 324, 324, 325, 325, 326, 
326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, 
335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 340, 341, 341, 342, 342, 343, 343, 344, 
344, 345, 345, 346, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, 
353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 361, 362, 362, 
363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 371, 372, 
372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, 
382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, 
392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 401, 401, 402, 
402, 403, 403, 404, 404, 405, 405, 406, 406, 407, 407, 408, 408, 409, 409, 410, 410, 411, 411, 412, 
412, 413, 413, 414, 414, 415, 415, 416, 416, 417, 417, 418, 418, 419, 419, 420, 420, 421, 421, 422, 
423, 423, 424, 424, 425, 425, 426, 426, 427, 427, 428, 428, 429, 429, 430, 430, 431, 431, 432, 432, 
433, 433, 434, 435, 435, 436, 436, 437, 437, 438, 438, 439, 439, 440, 440, 441, 441, 442, 442, 443, 
444, 444, 445, 445, 446, 446, 447, 447, 448, 448, 449, 449, 450, 450, 451, 452, 452, 453, 453, 454, 
454, 455, 455, 456, 456, 457, 458, 458, 459, 459, 460, 460, 461, 461, 462, 462, 463, 464, 464, 465, 
465, 466, 466, 467, 467, 468, 468, 469, 470, 470, 471, 471, 472, 472, 473, 473, 474, 475, 475, 476, 
476, 477, 477, 478, 478, 479, 480, 480, 481, 481, 482, 482, 483, 483, 484, 485, 485, 486, 486, 487, 
487, 488, 488, 489, 490, 490, 491, 491, 492, 492, 493, 494, 494, 495, 495, 496, 496, 497, 498, 498, 
499, 499, 500, 500, 501, 502, 502, 503, 503, 504, 504, 505, 506, 506, 507, 507, 508, 508, 509, 510, 
510, 511, 511, 512, 512, 513, 514, 514, 515, 515, 516, 517, 517, 518, 518, 519, 519, 520, 521, 521, 
522, 522, 523, 524, 524, 525, 525, 526, 526, 527, 528, 528, 529, 529, 530, 531, 531, 532, 532, 533, 
534, 534, 535, 535, 536, 537, 537, 538, 538, 539, 539, 540, 541, 541, 542, 542, 543, 544, 544, 545, 
545, 546, 547, 547, 548, 548, 549, 550, 550, 551, 551, 552, 553, 553, 554, 555, 555, 556, 556, 557, 
558, 558, 559, 559, 560, 561, 561, 562, 562, 563, 564, 564, 565, 565, 566, 567, 567, 568, 569, 569, 
570, 570, 571, 572, 572, 573, 573, 574, 575, 575, 576, 577, 577, 578, 578, 579, 580, 580, 581, 582, 
582, 583, 583, 584, 585, 585, 586, 586, 587, 588, 588, 589, 590, 590, 591, 591, 592, 593, 593, 594, 
595, 595, 596, 597, 597, 598, 598, 599, 600, 600, 601, 602, 602, 603, 603, 604, 605, 605, 606, 607, 
607, 608, 609, 609, 610, 610, 611, 612, 612, 613, 614, 614, 615, 616, 616, 617, 618, 618, 619, 619, 
620, 621, 621, 622, 623, 623, 624, 625, 625, 626, 627, 627, 628, 629, 629, 630, 630, 631, 632, 632, 
633, 634, 634, 635, 636, 636, 637, 638, 638, 639, 640, 640, 641, 642, 642, 643, 644, 644, 645, 646, 
646, 647, 647, 648, 649, 649, 650, 651, 651, 652, 653, 653, 654, 655, 655, 656, 657, 657, 658, 659, 
659, 660, 661, 661, 662, 663, 663, 664, 665, 665, 666, 667, 667, 668, 669, 669, 670, 671, 671, 672, 
673, 674, 674, 675, 676, 676, 677, 678, 678, 679, 680, 680, 681, 682, 682, 683, 684, 684, 685, 686, 
686, 687, 688, 688, 689, 690, 690, 691, 692, 693, 693, 694, 695, 695, 696, 697, 697, 698, 699, 699, 
700, 701, 701, 702, 703, 704, 704, 705, 706, 706, 707, 708, 708, 709, 710, 710, 711, 712, 713, 713, 
714, 715, 715, 716, 717, 717, 718, 719, 719, 720, 721, 722, 722, 723, 724, 724, 725, 726, 726, 727, 
728, 729, 729, 730, 731, 731, 732, 733, 734, 734, 735, 736, 736, 737, 738, 738, 739, 740, 741, 741, 
742, 743, 743, 744, 745, 746, 746, 747, 748, 748, 749, 750, 751, 751, 752, 753, 753, 754, 755, 756, 
756, 757, 758, 758, 759, 760, 761, 761, 762, 763, 763, 764, 765, 766, 766, 767, 768, 769, 769, 770, 
771, 771, 772, 773, 774, 774, 775, 776, 777, 777, 778, 779, 779, 780, 781, 782, 782, 783, 784, 785, 
785, 786, 787, 787, 788, 789, 790, 790, 791, 792, 793, 793, 794, 795, 796, 796, 797, 798, 798, 799, 
800, 801, 801, 802, 803, 804, 804, 805, 806, 807, 807, 808, 809, 810, 810, 811, 812, 813, 813, 814, 
815, 816, 816, 817, 818, 819, 819, 820, 821, 822, 822, 823, 824, 825, 825, 826, 827, 828, 828, 829, 
830, 831, 831, 832, 833, 834, 834, 835, 836, 837, 837, 838, 839, 840, 840, 841, 842, 843, 843, 844, 
845, 846, 846, 847, 848, 849, 849, 850, 851, 852, 853, 853, 854, 855, 856, 856, 857, 858, 859, 859, 
860, 861, 862, 862, 863, 864, 865, 866, 866, 867, 868, 869, 869, 870, 871, 872, 872, 873, 874, 875, 
876, 876, 877, 878, 879, 879, 880, 881, 882, 883, 883, 884, 885, 886, 886, 887, 888, 889, 890, 890, 
891, 892, 893, 893, 894, 895, 896, 897, 897, 898, 899, 900, 900, 901, 902, 903, 904, 904, 905, 906, 
907, 908, 908, 909, 910, 911, 911, 912, 913, 914, 915, 915, 916, 917, 918, 919, 919, 920, 921, 922, 
923, 923, 924, 925, 926, 927, 927, 928, 929, 930, 931, 931, 932, 933, 934, 935, 935, 936, 937, 938, 
939, 939, 940, 941, 942, 943, 943, 944, 945, 946, 947, 947, 948, 949, 950, 951, 951, 952, 953, 954, 
955, 955, 956, 957, 958, 959, 959, 960, 961, 962, 963, 963, 964, 965, 966, 967, 968, 968, 969, 970, 
971, 972, 972, 973, 974, 975, 976, 976, 977, 978, 979, 980, 981, 981, 982, 983, 984, 985, 985, 986, 
987, 988, 989, 990, 990, 991, 992, 993, 994, 994, 995, 996, 997, 998, 999, 999, 1000, 1001, 1002, 1003, 
1004, 1004, 1005, 1006, 1007, 1008, 1008, 1009, 1010, 1011, 1012, 1013, 1013, 1014, 1015, 1016, 1017, 1018, 1018, 1019, 
1020, 1021, 1022, 1023, 1023, 1024, 1025, 1026, 1027, 1028, 1028, 1029, 1030, 1031, 1032, 1033, 1033, 1034, 1035, 1036, 
1037, 1038, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1044, 1045, 1046, 1047, 1048, 1049, 1049, 1050, 1051, 1052, 1053, 
1054, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1060, 1061, 1062, 1063, 1064, 1065, 1065, 1066, 1067, 1068, 1069, 1070, 
1071, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1077, 1078, 1079, 1080, 1081, 1082, 1082, 1083, 1084, 1085, 1086, 1087, 
1088, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1100, 1101, 1102, 1103, 1104, 
1105, 1106, 1107, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1119, 1120, 1121, 
1122, 1123, 1124, 1125, 1126, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 
1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1153, 1154, 1155, 1156, 
1157, 1158, 1159, 1160, 1161, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 
1175, 1176, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1191, 
1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1208, 1209, 
1210, 1211, 1212, 1213, 1214, 1215, 1216, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1225, 1226, 1227, 
1228, 1229, 1230, 1231, 1232, 1233, 1234, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1243, 1244, 1245, 
1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1263, 
1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 1280, 1281, 1282, 
1283, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 1290, 1291, 1292, 1293, 1294, 1294, 1295, 1296, 1297, 1298, 1299, 1300, 
1301, 1302, 1303, 1304, 1305, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1317, 1318, 
1319, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 
1338, 1339, 1340, 1341, 1342, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 
1356, 1357, 1358, 1359, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 1370, 1370, 1371, 1372, 1373, 1374, 
1375, 1376, 1377, 1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385, 1385, 1386, 1387, 1388, 1389, 1390, 1391, 1392, 1393, 
1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 1410, 1411, 1412, 
1413, 1414, 1415, 1416, 1417, 1417, 1418, 1419, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 
1432, 1433, 1434, 1435, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 
1451, 1452, 1453, 1454, 1455, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 
1470, 1471, 1472, 1473, 1474, 1475, 1476, 1476, 1477, 1478, 1479, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 
1489, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 1500, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 
1508, 1509, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1526, 
1527, 1528, 1529, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 
1547, 1548, 1549, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1556, 1557, 1558, 1559, 1560, 1561, 1562, 1563, 1564, 1565, 
1566, 1567, 1568, 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 1580, 1581, 1582, 1583, 1584, 1585, 
1586, 1587, 1588, 1589, 1590, 1591, 1592, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 1600, 1601, 1602, 1603, 1604, 
1605, 1606, 1607, 1608, 1609, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 1620, 1621, 1622, 1623, 1624, 
1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1637, 1638, 1639, 1640, 1641, 1642, 1643, 
1644, 1645, 1646, 1647, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1663, 
1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 1680, 1681, 1682, 1683, 
1684, 1685, 1686, 1687, 1688, 1689, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 1700, 1701, 1702, 1702, 
1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, 
1723, 1724, 1725, 1726, 1727, 1728, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 1740, 1741, 1742, 
1743, 1744, 1745, 1746, 1747, 1748, 1749, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 1762, 
1763, 1764, 1765, 1766, 1767, 1768, 1769, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 1780, 1781, 1782, 
1783, 1784, 1785, 1786, 1787, 1788, 1789, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, 1801, 1802, 
1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 1820, 1821, 1822, 
1823, 1824, 1825, 1826, 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 
1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 
1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 
1883, 1884, 1885, 1886, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, 
1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, 
1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 
1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 
1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 
1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 
2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 
2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 2040, 2041, 
2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 2060, 2061, 
2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 2080, 2081, 
2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 2100, 2101, 
2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 2120, 2121, 
2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 2140, 2141, 
2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 2160, 2161, 
2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 2180, 2181, 
2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 2200, 2201, 
2202, 2203, 2204, 2205, 2205, 2206, 2207, 2208, 2209, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 2220, 
2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240, 
2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 2260, 
2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 2270, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 
2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 
2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 2310, 2311, 2312, 2313, 2314, 2315, 2315, 2316, 2317, 2318, 
2319, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 
2339, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 2350, 2351, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 
2358, 2359, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 
2378, 2379, 2380, 2381, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 
2397, 2398, 2399, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2407, 2408, 2409, 2410, 2411, 2412, 2413, 2414, 2415, 
2416, 2417, 2418, 2419, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 2430, 2431, 2431, 2432, 2433, 2434, 
2435, 2436, 2437, 2438, 2439, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 2450, 2451, 2452, 2452, 2453, 
2454, 2455, 2456, 2457, 2458, 2459, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 2470, 2471, 2472, 2472, 
2473, 2474, 2475, 2476, 2477, 2478, 2479, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 2490, 2490, 2491, 
2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2506, 2507, 2508, 2509, 2510, 
2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 2520, 2521, 2522, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 
2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2537, 2538, 2539, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 
2549, 2550, 2551, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2565, 2566, 
2567, 2568, 2569, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2578, 2579, 2580, 2581, 2582, 2583, 2584, 2585, 
2586, 2587, 2588, 2589, 2590, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 2600, 2601, 2602, 2602, 2603, 
2604, 2605, 2606, 2607, 2608, 2609, 2610, 2611, 2612, 2613, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 2620, 2621, 2622, 
2623, 2624, 2624, 2625, 2626, 2627, 2628, 2629, 2630, 2631, 2632, 2633, 2634, 2634, 2635, 2636, 2637, 2638, 2639, 2640, 
2641, 2642, 2643, 2644, 2644, 2645, 2646, 2647, 2648, 2649, 2650, 2651, 2652, 2653, 2654, 2654, 2655, 2656, 2657, 2658, 
2659, 2660, 2661, 2662, 2663, 2664, 2664, 2665, 2666, 2667, 2668, 2669, 2670, 2671, 2672, 2673, 2673, 2674, 2675, 2676, 
2677, 2678, 2679, 2680, 2681, 2682, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 2690, 2691, 2691, 2692, 2693, 2694, 
2695, 2696, 2697, 2698, 2699, 2699, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2708, 2709, 2710, 2711, 2712, 
2713, 2714, 2715, 2716, 2716, 2717, 2718, 2719, 2720, 2721, 2722, 2723, 2724, 2724, 2725, 2726, 2727, 2728, 2729, 2730, 
2731, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 2739, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2746, 2747, 
2748, 2749, 2750, 2751, 2752, 2753, 2754, 2754, 2755, 2756, 2757, 2758, 2759, 2760, 2761, 2761, 2762, 2763, 2764, 2765, 
2766, 2767, 2768, 2768, 2769, 2770, 2771, 2772, 2773, 2774, 2774, 2775, 2776, 2777, 2778, 2779, 2780, 2781, 2781, 2782, 
2783, 2784, 2785, 2786, 2787, 2788, 2788, 2789, 2790, 2791, 2792, 2793, 2794, 2794, 2795, 2796, 2797, 2798, 2799, 2800, 
2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2807, 2808, 2809, 2810, 2811, 2812, 2813, 2813, 2814, 2815, 2816, 2817, 
2818, 2819, 2819, 2820, 2821, 2822, 2823, 2824, 2825, 2825, 2826, 2827, 2828, 2829, 2830, 2830, 2831, 2832, 2833, 2834, 
2835, 2836, 2836, 2837, 2838, 2839, 2840, 2841, 2842, 2842, 2843, 2844, 2845, 2846, 2847, 2847, 2848, 2849, 2850, 2851, 
2852, 2853, 2853, 2854, 2855, 2856, 2857, 2858, 2858, 2859, 2860, 2861, 2862, 2863, 2863, 2864, 2865, 2866, 2867, 2868, 
2869, 2869, 2870, 2871, 2872, 2873, 2874, 2874, 2875, 2876, 2877, 2878, 2879, 2879, 2880, 2881, 2882, 2883, 2884, 2884, 
2885, 2886, 2887, 2888, 2889, 2889, 2890, 2891, 2892, 2893, 2894, 2894, 2895, 2896, 2897, 2898, 2899, 2899, 2900, 2901, 
2902, 2903, 2903, 2904, 2905, 2906, 2907, 2908, 2908, 2909, 2910, 2911, 2912, 2913, 2913, 2914, 2915, 2916, 2917, 2917, 
2918, 2919, 2920, 2921, 2922, 2922, 2923, 2924, 2925, 2926, 2926, 2927, 2928, 2929, 2930, 2931, 2931, 2932, 2933, 2934, 
2935, 2935, 2936, 2937, 2938, 2939, 2939, 2940, 2941, 2942, 2943, 2944, 2944, 2945, 2946, 2947, 2948, 2948, 2949, 2950, 
2951, 2952, 2952, 2953, 2954, 2955, 2956, 2956, 2957, 2958, 2959, 2960, 2960, 2961, 2962, 2963, 2964, 2964, 2965, 2966, 
2967, 2968, 2968, 2969, 2970, 2971, 2972, 2972, 2973, 2974, 2975, 2976, 2976, 2977, 2978, 2979, 2980, 2980, 2981, 2982, 
2983, 2984, 2984, 2985, 2986, 2987, 2988, 2988, 2989, 2990, 2991, 2992, 2992, 2993, 2994, 2995, 2996, 2996, 2997, 2998, 
2999, 2999, 3000, 3001, 3002, 3003, 3003, 3004, 3005, 3006, 3007, 3007, 3008, 3009, 3010, 3010, 3011, 3012, 3013, 3014, 
3014, 3015, 3016, 3017, 3017, 3018, 3019, 3020, 3021, 3021, 3022, 3023, 3024, 3024, 3025, 3026, 3027, 3028, 3028, 3029, 
3030, 3031, 3031, 3032, 3033, 3034, 3035, 3035, 3036, 3037, 3038, 3038, 3039, 3040, 3041, 3041, 3042, 3043, 3044, 3045, 
3045, 3046, 3047, 3048, 3048, 3049, 3050, 3051, 3051, 3052, 3053, 3054, 3054, 3055, 3056, 3057, 3058, 3058, 3059, 3060, 
3061, 3061, 3062, 3063, 3064, 3064, 3065, 3066, 3067, 3067, 3068, 3069, 3070, 3070, 3071, 3072, 3073, 3073, 3074, 3075, 
3076, 3076, 3077, 3078, 3079, 3079, 3080, 3081, 3082, 3082, 3083, 3084, 3085, 3085, 3086, 3087, 3088, 3088, 3089, 3090, 
3091, 3091, 3092, 3093, 3094, 3094, 3095, 3096, 3097, 3097, 3098, 3099, 3100, 3100, 3101, 3102, 3103, 3103, 3104, 3105, 
3106, 3106, 3107, 3108, 3109, 3109, 3110, 3111, 3111, 3112, 3113, 3114, 3114, 3115, 3116, 3117, 3117, 3118, 3119, 3120, 
3120, 3121, 3122, 3122, 3123, 3124, 3125, 3125, 3126, 3127, 3128, 3128, 3129, 3130, 3130, 3131, 3132, 3133, 3133, 3134, 
3135, 3136, 3136, 3137, 3138, 3138, 3139, 3140, 3141, 3141, 3142, 3143, 3144, 3144, 3145, 3146, 3146, 3147, 3148, 3149, 
3149, 3150, 3151, 3151, 3152, 3153, 3154, 3154, 3155, 3156, 3156, 3157, 3158, 3159, 3159, 3160, 3161, 3161, 3162, 3163, 
3164, 3164, 3165, 3166, 3166, 3167, 3168, 3169, 3169, 3170, 3171, 3171, 3172, 3173, 3173, 3174, 3175, 3176, 3176, 3177, 
3178, 3178, 3179, 3180, 3181, 3181, 3182, 3183, 3183, 3184, 3185, 3185, 3186, 3187, 3188, 3188, 3189, 3190, 3190, 3191, 
3192, 3192, 3193, 3194, 3194, 3195, 3196, 3197, 3197, 3198, 3199, 3199, 3200, 3201, 3201, 3202, 3203, 3203, 3204, 3205, 
3206, 3206, 3207, 3208, 3208, 3209, 3210, 3210, 3211, 3212, 3212, 3213, 3214, 3214, 3215, 3216, 3217, 3217, 3218, 3219, 
3219, 3220, 3221, 3221, 3222, 3223, 3223, 3224, 3225, 3225, 3226, 3227, 3227, 3228, 3229, 3229, 3230, 3231, 3231, 3232, 
3233, 3233, 3234, 3235, 3236, 3236, 3237, 3238, 3238, 3239, 3240, 3240, 3241, 3242, 3242, 3243, 3244, 3244, 3245, 3246, 
3246, 3247, 3248, 3248, 3249, 3250, 3250, 3251, 3252, 3252, 3253, 3254, 3254, 3255, 3256, 3256, 3257, 3258, 3258, 3259, 
3260, 3260, 3261, 3261, 3262, 3263, 3263, 3264, 3265, 3265, 3266, 3267, 3267, 3268, 3269, 3269, 3270, 3271, 3271, 3272, 
3273, 3273, 3274, 3275, 3275, 3276, 3277, 3277, 3278, 3278, 3279, 3280, 3280, 3281, 3282, 3282, 3283, 3284, 3284, 3285, 
3286, 3286, 3287, 3288, 3288, 3289, 3289, 3290, 3291, 3291, 3292, 3293, 3293, 3294, 3295, 3295, 3296, 3297, 3297, 3298, 
3298, 3299, 3300, 3300, 3301, 3302, 3302, 3303, 3304, 3304, 3305, 3305, 3306, 3307, 3307, 3308, 3309, 3309, 3310, 3310, 
3311, 3312, 3312, 3313, 3314, 3314, 3315, 3316, 3316, 3317, 3317, 3318, 3319, 3319, 3320, 3321, 3321, 3322, 3322, 3323, 
3324, 3324, 3325, 3325, 3326, 3327, 3327, 3328, 3329, 3329, 3330, 3330, 3331, 3332, 3332, 3333, 3334, 3334, 3335, 3335, 
3336, 3337, 3337, 3338, 3338, 3339, 3340, 3340, 3341, 3342, 3342, 3343, 3343, 3344, 3345, 3345, 3346, 3346, 3347, 3348, 
3348, 3349, 3349, 3350, 3351, 3351, 3352, 3352, 3353, 3354, 3354, 3355, 3356, 3356, 3357, 3357, 3358, 3359, 3359, 3360, 
3360, 3361, 3362, 3362, 3363, 3363, 3364, 3365, 3365, 3366, 3366, 3367, 3368, 3368, 3369, 3369, 3370, 3370, 3371, 3372, 
3372, 3373, 3373, 3374, 3375, 3375, 3376, 3376, 3377, 3378, 3378, 3379, 3379, 3380, 3381, 3381, 3382, 3382, 3383, 3383, 
3384, 3385, 3385, 3386, 3386, 3387, 3388, 3388, 3389, 3389, 3390, 3390, 3391, 3392, 3392, 3393, 3393, 3394, 3395, 3395, 
3396, 3396, 3397, 3397, 3398, 3399, 3399, 3400, 3400, 3401, 3401, 3402, 3403, 3403, 3404, 3404, 3405, 3405, 3406, 3407, 
3407, 3408, 3408, 3409, 3409, 3410, 3411, 3411, 3412, 3412, 3413, 3413, 3414, 3415, 3415, 3416, 3416, 3417, 3417, 3418, 
3419, 3419, 3420, 3420, 3421, 3421, 3422, 3422, 3423, 3424, 3424, 3425, 3425, 3426, 3426, 3427, 3427, 3428, 3429, 3429, 
3430, 3430, 3431, 3431, 3432, 3432, 3433, 3434, 3434, 3435, 3435, 3436, 3436, 3437, 3437, 3438, 3439, 3439, 3440, 3440, 
3441, 3441, 3442, 3442, 3443, 3443, 3444, 3445, 3445, 3446, 3446, 3447, 3447, 3448, 3448, 3449, 3449, 3450, 3451, 3451, 
3452, 3452, 3453, 3453, 3454, 3454, 3455, 3455, 3456, 3457, 3457, 3458, 3458, 3459, 3459, 3460, 3460, 3461, 3461, 3462, 
3462, 3463, 3463, 3464, 3465, 3465, 3466, 3466, 3467, 3467, 3468, 3468, 3469, 3469, 3470, 3470, 3471, 3471, 3472, 3472, 
3473, 3474, 3474, 3475, 3475, 3476, 3476, 3477, 3477, 3478, 3478, 3479, 3479, 3480, 3480, 3481, 3481, 3482, 3482, 3483, 
3483, 3484, 3484, 3485, 3486, 3486, 3487, 3487, 3488, 3488, 3489, 3489, 3490, 3490, 3491, 3491, 3492, 3492, 3493, 3493, 
3494, 3494, 3495, 3495, 3496, 3496, 3497, 3497, 3498, 3498, 3499, 3499, 3500, 3500, 3501, 3501, 3502, 3502, 3503, 3503, 
3504, 3504, 3505, 3505, 3506, 3506, 3507, 3507, 3508, 3508, 3509, 3509, 3510, 3510, 3511, 3511, 3512, 3512, 3513, 3513, 
3514, 3514, 3515, 3515, 3516, 3516, 3517, 3517, 3518, 3518, 3519, 3519, 3520, 3520, 3521, 3521, 3522, 3522, 3523, 3523, 
3524, 3524, 3525, 3525, 3526, 3526, 3527, 3527, 3528, 3528, 3529, 3529, 3530, 3530, 3531, 3531, 3532, 3532, 3533, 3533, 
3534, 3534, 3535, 3535, 3536, 3536, 3536, 3537, 3537, 3538, 3538, 3539, 3539, 3540, 3540, 3541, 3541, 3542, 3542, 3543, 
3543, 3544, 3544, 3545, 3545, 3546, 3546, 3546, 3547, 3547, 3548, 3548, 3549, 3549, 3550, 3550, 3551, 3551, 3552, 3552, 
3553, 3553, 3554, 3554, 3554, 3555, 3555, 3556, 3556, 3557, 3557, 3558, 3558, 3559, 3559, 3560, 3560, 3561, 3561, 3561, 
3562, 3562, 3563, 3563, 3564, 3564, 3565, 3565, 3566, 3566, 3567, 3567, 3567, 3568, 3568, 3569, 3569, 3570, 3570, 3571, 
3571, 3572, 3572, 3572, 3573, 3573, 3574, 3574, 3575, 3575, 3576, 3576, 3577, 3577, 3577, 3578, 3578, 3579, 3579, 3580, 
3580, 3581, 3581, 3581, 3582, 3582, 3583, 3583, 3584, 3584, 3585, 3585, 3585, 3586, 3586, 3587, 3587, 3588, 3588, 3589, 
3589, 3589, 3590, 3590, 3591, 3591, 3592, 3592, 3593, 3593, 3593, 3594, 3594, 3595, 3595, 3596, 3596, 3596, 3597, 3597, 
3598, 3598, 3599, 3599, 3600, 3600, 3600, 3601, 3601, 3602, 3602, 3603, 3603, 3603, 3604, 3604, 3605, 3605, 3606, 3606, 
3606, 3607, 3607, 3608, 3608, 3609, 3609, 3609, 3610, 3610, 3611, 3611, 3611, 3612, 3612, 3613, 3613, 3614, 3614, 3614, 
3615, 3615, 3616, 3616, 3617, 3617, 3617, 3618, 3618, 3619, 3619, 3619, 3620, 3620, 3621, 3621, 3622, 3622, 3622, 3623, 
3623, 3624, 3624, 3624, 3625, 3625, 3626, 3626, 3627, 3627, 3627, 3628, 3628, 3629, 3629, 3629, 3630, 3630, 3631, 3631, 
3631, 3632, 3632, 3633, 3633, 3633, 3634, 3634, 3635, 3635, 3635, 3636, 3636, 3637, 3637, 3637, 3638, 3638, 3639, 3639, 
3639, 3640, 3640, 3641, 3641, 3641, 3642, 3642, 3643, 3643, 3643, 3644, 3644, 3645, 3645, 3645, 3646, 3646, 3647, 3647, 
3647, 3648, 3648, 3649, 3649, 3649, 3650, 3650, 3651, 3651, 3651, 3652, 3652, 3653, 3653, 3653, 3654, 3654, 3654, 3655, 
3655, 3656, 3656, 3656, 3657, 3657, 3658, 3658, 3658, 3659, 3659, 3659, 3660, 3660, 3661, 3661, 3661, 3662, 3662, 3663, 
3663, 3663, 3664, 3664, 3664, 3665, 3665, 3666, 3666, 3666, 3667, 3667, 3667, 3668, 3668, 3669, 3669, 3669, 3670, 3670, 
3670, 3671, 3671, 3672, 3672, 3672, 3673, 3673, 3673, 3674, 3674, 3675, 3675, 3675, 3676, 3676, 3676, 3677, 3677, 3678, 
3678, 3678, 3679, 3679, 3679, 3680, 3680, 3680, 3681, 3681, 3682, 3682, 3682, 3683, 3683, 3683, 3684, 3684, 3684, 3685, 
3685, 3686, 3686, 3686, 3687, 3687, 3687, 3688, 3688, 3688, 3689, 3689, 3690, 3690, 3690, 3691, 3691, 3691, 3692, 3692, 
3692, 3693, 3693, 3693, 3694, 3694, 3694, 3695, 3695, 3696, 3696, 3696, 3697, 3697, 3697, 3698, 3698, 3698, 3699, 3699, 
3699, 3700, 3700, 3700, 3701, 3701, 3701, 3702, 3702, 3703, 3703, 3703, 3704, 3704, 3704, 3705, 3705, 3705, 3706, 3706, 
3706, 3707, 3707, 3707, 3708, 3708, 3708, 3709, 3709, 3709, 3710, 3710, 3710, 3711, 3711, 3711, 3712, 3712, 3712, 3713, 
3713, 3713, 3714, 3714, 3714, 3715, 3715, 3715, 3716, 3716, 3716, 3717, 3717, 3717, 3718, 3718, 3718, 3719, 3719, 3719, 
3720, 3720, 3720, 3721, 3721, 3721, 3722, 3722, 3722, 3723, 3723, 3723, 3724, 3724, 3724, 3725, 3725, 3725, 3726, 3726, 
3726, 3727, 3727, 3727, 3728, 3728, 3728, 3729, 3729, 3729, 3730, 3730, 3730, 3731, 3731, 3731, 3731, 3732, 3732, 3732, 
3733, 3733, 3733, 3734, 3734, 3734, 3735, 3735, 3735, 3736, 3736, 3736, 3737, 3737, 3737, 3738, 3738, 3738, 3738, 3739, 
3739, 3739, 3740, 3740, 3740, 3741, 3741, 3741, 3742, 3742, 3742, 3743, 3743, 3743, 3743, 3744, 3744, 3744, 3745, 3745, 
3745, 3746, 3746, 3746, 3747, 3747, 3747, 3747, 3748, 3748, 3748, 3749, 3749, 3749, 3750, 3750, 3750, 3750, 3751, 3751, 
3751, 3752, 3752, 3752, 3753, 3753, 3753, 3753, 3754, 3754, 3754, 3755, 3755, 3755, 3756, 3756, 3756, 3756, 3757, 3757, 
3757, 3758, 3758, 3758, 3759, 3759, 3759, 3759, 3760, 3760, 3760, 3761, 3761, 3761, 3761, 3762, 3762, 3762, 3763, 3763, 
3763, 3763, 3764, 3764, 3764, 3765, 3765, 3765, 3766, 3766, 3766, 3766, 3767, 3767, 3767, 3768, 3768, 3768, 3768, 3769, 
3769, 3769, 3770, 3770, 3770, 3770, 3771, 3771, 3771, 3771, 3772, 3772, 3772, 3773, 3773, 3773, 3773, 3774, 3774, 3774, 
3775, 3775, 3775, 3775, 3776, 3776, 3776, 3777, 3777, 3777, 3777, 3778, 3778, 3778, 3778, 3779, 3779, 3779, 3780, 3780, 
3780, 3780, 3781, 3781, 3781, 3781, 3782, 3782, 3782, 3783, 3783, 3783, 3783, 3784, 3784, 3784, 3784, 3785, 3785, 3785, 
3786, 3786, 3786, 3786, 3787, 3787, 3787, 3787, 3788, 3788, 3788, 3788, 3789, 3789, 3789, 3790, 3790, 3790, 3790, 3791, 
3791, 3791, 3791, 3792, 3792, 3792, 3792, 3793, 3793, 3793, 3793, 3794, 3794, 3794, 3794, 3795, 3795, 3795, 3796, 3796, 
3796, 3796, 3797, 3797, 3797, 3797, 3798, 3798, 3798, 3798, 3799, 3799, 3799, 3799, 3800, 3800, 3800, 3800, 3801, 3801, 
3801, 3801, 3802, 3802, 3802, 3802, 3803, 3803, 3803, 3803, 3804, 3804, 3804, 3804, 3805, 3805, 3805, 3805, 3806, 3806, 
3806, 3806, 3807, 3807, 3807, 3807, 3808, 3808, 3808, 3808, 3809, 3809, 3809, 3809, 3810, 3810, 3810, 3810, 3811, 3811, 
3811, 3811, 3812, 3812, 3812, 3812, 3812, 3813, 3813, 3813, 3813, 3814, 3814, 3814, 3814, 3815, 3815, 3815, 3815, 3816, 
3816, 3816, 3816, 3817, 3817, 3817, 3817, 3818, 3818, 3818, 3818, 3818, 3819, 3819, 3819, 3819, 3820, 3820, 3820, 3820, 
3821, 3821, 3821, 3821, 3821, 3822, 3822, 3822, 3822, 3823, 3823, 3823, 3823, 3824, 3824, 3824, 3824, 3824, 3825, 3825, 
3825, 3825, 3826, 3826, 3826, 3826, 3827, 3827, 3827, 3827, 3827, 3828, 3828, 3828, 3828, 3829, 3829, 3829, 3829, 3829, 
3830, 3830, 3830, 3830, 3831, 3831, 3831, 3831, 3831, 3832, 3832, 3832, 3832, 3833, 3833, 3833, 3833, 3833, 3834, 3834, 
3834, 3834, 3835, 3835, 3835, 3835, 3835, 3836, 3836, 3836, 3836, 3836, 3837, 3837, 3837, 3837, 3838, 3838, 3838, 3838, 
3838, 3839, 3839, 3839, 3839, 3839, 3840, 3840, 3840, 3840, 3841, 3841, 3841, 3841, 3841, 3842, 3842, 3842, 3842, 3842, 
3843, 3843, 3843, 3843, 3843, 3844, 3844, 3844, 3844, 3844, 3845, 3845, 3845, 3845, 3846, 3846, 3846, 3846, 3846, 3847, 
3847, 3847, 3847, 3847, 3848, 3848, 3848, 3848, 3848, 3849, 3849, 3849, 3849, 3849, 3850, 3850, 3850, 3850, 3850, 3851, 
3851, 3851, 3851, 3851, 3852, 3852, 3852, 3852, 3852, 3853, 3853, 3853, 3853, 3853, 3854, 3854, 3854, 3854, 3854, 3855, 
3855, 3855, 3855, 3855, 3856, 3856, 3856, 3856, 3856, 3857, 3857, 3857, 3857, 3857, 3857, 3858, 3858, 3858, 3858, 3858, 
3859, 3859, 3859, 3859, 3859, 3860, 3860, 3860, 3860, 3860, 3861, 3861, 3861, 3861, 3861, 3861, 3862, 3862, 3862, 3862, 
3862, 3863, 3863, 3863, 3863, 3863, 3864, 3864, 3864, 3864, 3864, 3864, 3865, 3865, 3865, 3865, 3865, 3866, 3866, 3866, 
3866, 3866, 3867, 3867, 3867, 3867, 3867, 3867, 3868, 3868, 3868, 3868, 3868, 3868, 3869, 3869, 3869, 3869, 3869, 3870, 
3870, 3870, 3870, 3870, 3870, 3871, 3871, 3871, 3871, 3871, 3872, 3872, 3872, 3872, 3872, 3872, 3873, 3873, 3873, 3873, 
3873, 3873, 3874, 3874, 3874, 3874, 3874, 3875, 3875, 3875, 3875, 3875, 3875, 3876, 3876, 3876, 3876, 3876, 3876, 3877, 
3877, 3877, 3877, 3877, 3877, 3878, 3878, 3878, 3878, 3878, 3878, 3879, 3879, 3879, 3879, 3879, 3879, 3880, 3880, 3880, 
3880, 3880, 3880, 3881, 3881, 3881, 3881, 3881, 3881, 3882, 3882, 3882, 3882, 3882, 3882, 3883, 3883, 3883, 3883, 3883, 
3883, 3884, 3884, 3884, 3884, 3884, 3884, 3885, 3885, 3885, 3885, 3885, 3885, 3886, 3886, 3886, 3886, 3886, 3886, 3887, 
3887, 3887, 3887, 3887, 3887, 3887, 3888, 3888, 3888, 3888, 3888, 3888, 3889, 3889, 3889, 3889, 3889, 3889, 3890, 3890, 
3890, 3890, 3890, 3890, 3890, 3891, 3891, 3891, 3891, 3891, 3891, 3892, 3892, 3892, 3892, 3892, 3892, 3892, 3893, 3893, 
3893, 3893, 3893, 3893, 3894, 3894, 3894, 3894, 3894, 3894, 3894, 3895, 3895, 3895, 3895, 3895, 3895, 3895, 3896, 3896, 
3896, 3896, 3896, 3896, 3897, 3897, 3897, 3897, 3897, 3897, 3897, 3898, 3898, 3898, 3898, 3898, 3898, 3898, 3899, 3899, 
3899, 3899, 3899, 3899, 3899, 3900, 3900, 3900, 3900, 3900, 3900, 3900, 3901, 3901, 3901, 3901, 3901, 3901, 3901, 3902, 
3902, 3902, 3902, 3902, 3902, 3902, 3903, 3903, 3903, 3903, 3903, 3903, 3903, 3904, 3904, 3904, 3904, 3904, 3904, 3904, 
3905, 3905, 3905, 3905, 3905, 3905, 3905, 3906, 3906, 3906, 3906, 3906, 3906, 3906, 3906, 3907, 3907, 3907, 3907, 3907, 
3907, 3907, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3909, 3909, 3909, 3909, 3909, 3909, 3909, 3910, 3910, 3910, 
3910, 3910, 3910, 3910, 3910, 3911, 3911, 3911, 3911, 3911, 3911, 3911, 3912, 3912, 3912, 3912, 3912, 3912, 3912, 3912, 
3913, 3913, 3913, 3913, 3913, 3913, 3913, 3913, 3914, 3914, 3914, 3914, 3914, 3914, 3914, 3914, 3915, 3915, 3915, 3915, 
3915, 3915, 3915, 3915, 3916, 3916, 3916, 3916, 3916, 3916, 3916, 3916, 3917, 3917, 3917, 3917, 3917, 3917, 3917, 3917, 
3918, 3918, 3918, 3918, 3918, 3918, 3918, 3918, 3919, 3919, 3919, 3919, 3919, 3919, 3919, 3919, 3919, 3920, 3920, 3920, 
3920, 3920, 3920, 3920, 3920, 3921, 3921, 3921, 3921, 3921, 3921, 3921, 3921, 3922, 3922, 3922, 3922, 3922, 3922, 3922, 
3922, 3922, 3923, 3923, 3923, 3923, 3923, 3923, 3923, 3923, 3923, 3924, 3924, 3924, 3924, 3924, 3924, 3924, 3924, 3925, 
3925, 3925, 3925, 3925, 3925, 3925, 3925, 3925, 3926, 3926, 3926, 3926, 3926, 3926, 3926, 3926, 3926, 3927, 3927, 3927, 
3927, 3927, 3927, 3927, 3927, 3927, 3928, 3928, 3928, 3928, 3928, 3928, 3928, 3928, 3928, 3929, 3929, 3929, 3929, 3929, 
3929, 3929, 3929, 3929, 3929, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3931, 3931, 3931, 3931, 3931, 3931, 
3931, 3931, 3931, 3931, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3933, 3933, 3933, 3933, 3933, 3933, 3933, 
3933, 3933, 3933, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3935, 3935, 3935, 3935, 3935, 3935, 3935, 
3935, 3935, 3935, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3937, 3937, 3937, 3937, 3937, 3937, 3937, 
3937, 3937, 3937, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3939, 3939, 3939, 3939, 3939, 3939, 
3939, 3939, 3939, 3939, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3941, 3941, 3941, 3941, 3941, 
3941, 3941, 3941, 3941, 3941, 3941, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3943, 3943, 3943, 
3943, 3943, 3943, 3943, 3943, 3943, 3943, 3943, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3945, 
3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3946, 3946, 3946, 3946, 3946, 3946, 3946, 3946, 3946, 
3946, 3946, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3948, 3948, 3948, 3948, 3948, 3948, 
3948, 3948, 3948, 3948, 3948, 3948, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3950, 
3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3951, 3951, 3951, 3951, 3951, 3951, 3951, 3951, 3951, 
3951, 3951, 3951, 3951, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3953, 3953, 3953, 
3953, 3953, 3953, 3953, 3953, 3953, 3953, 3953, 3953, 3953, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 
3954, 3954, 3954, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3956, 3956, 3956, 
3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3957, 3957, 3957, 3957, 3957, 3957, 3957, 3957, 3957, 
3957, 3957, 3957, 3957, 3957, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 
3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3960, 3960, 3960, 3960, 3960, 
3960, 3960, 3960, 3960, 3960, 3960, 3960, 3960, 3960, 3960, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 
3961, 3961, 3961, 3961, 3961, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 
3962, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3964, 3964, 3964, 
3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3965, 3965, 3965, 3965, 3965, 3965, 
3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 
3966, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 
3967, 3967, 3967, 3967, 3967, 3967, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 
3968, 3968, 3968, 3968, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 
3969, 3969, 3969, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 
3970, 3970, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 
3971, 3971, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 
3972, 3972, 3972, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 
3973, 3973, 3973, 3973, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 
3974, 3974, 3974, 3974, 3974, 3974, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 
3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 
3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 
3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3978, 3978, 3978, 3978, 
3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 
3978, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 
3979, 3979, 3979, 3979, 3979, 3979, 3979, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 
3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3981, 3981, 3981, 3981, 3981, 3981, 
3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 
3981, 3981, 3981};

    //****************************************
    // already #defined: N, I0, INVH, AMIN, AMAX
    #define ALPHA 1.83787706641  // = log(2*pi)
    double sim, simy, u;
    int k, ka, i;
    
    if (a<AMIN)  //if a is too small, use simple reject algorithm
        return ran_tg_reject(r,a);
    
    if (a>AMAX) // if a is too large, use Devroye's algorithm
        return ran_tg_devroye(r,a);

    i = I0+floor(a*INVH);
    ka = ncell[i];
    do {
      // sample integer between ka and N 
        k = ka+gsl_rng_uniform_int(r,N-ka+1); 
        if (k==N)  //right tail (last box on the right) 
                return ran_tg_devroye(r,x[N]); 
        if (k>ka+1)  {   // all the other boxes
            u = gsl_rng_uniform(r);
            simy = yu[k]*u;
            if (simy<yl[k]) { // that's what happens most of the time 
                sim = x[k]+u*delta[k];
                return sim;
            }
            // otherwise, check you're below the pdf curve
            sim = x[k]+d[k]*gsl_rng_uniform(r);
            if (sim*sim+2.*log(simy)+ALPHA<0.)
                return sim;
        }
	else {  // two leftmost regions 
            sim = x[k]+d[k]*gsl_rng_uniform(r);
            if (sim>=a) { //otherwise reject
                simy = yu[k]*gsl_rng_uniform(r);
                if (simy<yl[k])
                    return sim;
                if (sim*sim+2.*log(simy)+ALPHA<0.)
                    return sim;
                }
	}
    }
    while(1);

}


